some straightening out:--
OXXU8 MAAULGIHCTE
NOR
A PHONETIC NIGHTMARE
34. Here, as an awful warning to those who are ready to accept the
definition of English spelling given by a former headmaster of
Winchester--“Consonants are interchangeable, and vowels do not
count”--is a common English word of twelve letters, in “linked sweetness
long drawn out.”
Iewkngheaurrhphthewempeighghtips.
Can you decipher it?
ANOTHER WORD SQUARE
35. Can you, by filling in letters, complete this word square so that it
shall read alike across and from top to bottom?
* A * *
A * * A
* E * *
* A * E
A QUAINT INSCRIPTION
36. The following curious inscription may be seen on a card hanging up
in the bar of an old riverside inn in Norfolk:--
THEM * ILL * ERSLEA * VET * HEMI
LLT * HEW * HER * RYMEN * LOW
ERTH * EIRS * AILTH * EMA
LTS * TER * SLE * AVET * HE * KI
LN * FORAD * ROPO * FTH
EWHI * TESW * AN * SALE.
Can you decipher it?
A POET’S PI
37. TONDEBNIOTOCHUMFOARYHUR
OTDIRECTTHAWHOTERSOFKLSYA;
TIKATESTUBALIGHTSTILLETRUFLYR
OTBOWLALLNEFESLEAVARFWYAA.
In this printer’s pie the words are in their proper sequence, but the
letters are tangled.
BURIED PLACES
38. In the following short sentences five names of places are
buried--that is to say, the letters which spell them in proper order
form parts of more words than one. Thus, for example “Paris” might be
buried in the words “go u_p a ris_e:”
“The men could ride all on donkeys, the skipper, though, came to a bad
end.”
When you have discovered these places, try to find out what very
unexpected word of more than four letters is buried in the sentence, “On
Christmas Eve you rang out angel peals.”
TREASON CONDONED
39. According to an old poet, Sir John Harrington (1561-1612):--
“Treason doth never flourish; what’s the reason?
For if it prosper none dare call it treason!”
The classic lines may possibly have been the germ of the flippant modern
riddle, “Why is it no offence to conspire in the evening?”
A BIT OF BOTANY
40. Inscribe an _m_ above a line
And write an _e_ below,
This woodland flower is hung so fine
It bends when zephyrs flow.
A PIED PROVERB
41. The following letters, if they are properly rearranged, will fall
into the words which form a popular proverb:--
AAEEGGHILLMNNNOOOORRSSSSTT
Can you place them in position?
A DROP LETTER PUZZLE
42. Can you fill in the gaps of this proverb?
E**t* *e*s**s *a*e *h* *o** **i*e.
MULTUM IN PARVO
43. There is an English word of five syllables which has only eight
letters, five of them vowels--an a, an e, twice i, and y. What are its
consonants?
DOUBLETS
44. Can you turn TORMENT to RAPTURE, using four links, changing only one
letter each time, and varying the order of the letters?
A PIED PROVERB
45. Can you arrange these letters so that they form a sentence of five
words?
aaceeeffhhiiiiimnnoooprrssttttt.
The result is a well-known English proverb.
WHAT CAN IT BE?
46. Add one letter, and make this into a sensible English sentence:--
GDLDPRTFRRTHDXXFRDDNS
OUT OF PROPORTION
47. One vowel in an English word is found,
Which by eight consonants is hedged around.
48. Can you form an English word with these letters?
AAAAABBNNIIRSSTT.
49. What is this? It is found in Shakespeare:--
K I N I.
ALPHA BETA
50. There are two English words which contain each of them ten letters,
and six of these are a, b, c, d, e, f, the first six letters of the
alphabet. Can you build up either or both of them without looking at the
solution?
SHIFTING NUMBERS
51. Of a band of true kinsmen I stand at the head,
Who, to keep themselves warm, cluster three in a bed.
Put four into gaol and their number has risen,
So that six can be counted together in prison.
Take the six and recount them, they dwindle to three;
Count again, and a change into five you will see.
With no number from one to one hundred I mix,
Yet with five of my mates I am seen to make six.
AN IMPUDENT PRODIGAL
52. The prodigal son of a wealthy colonial farmer received a letter from
his father, to suggest that a considerable part of his inheritance
should be safeguarded before he squandered it. His reply ran
thus:--“Dear dad, keep 1000050.” As such a sum, even in dollars, was out
of the question, the father was completely puzzled.
What did the prodigal mean?
BURIED POETS
53. The names of eight famous British poets are buried in these lines,
that is to say, the letters that spell the names form in their proper
order parts of different words:--
The sun is darting rays of gold
Upon the moor, enchanting spot,
Whose purpled heights, by Ronald loved,
Up open to his Shepherd cot.
And sundry denizens of air
Are flying, aye, each to his nest;
And eager make at such an hour
All haste to reach the mansions-blest.
Can you dig them up?
A FATEFUL LETTER
54. When _A. B._ gave up the reins of government, and _C. B._ took
office in his place, it was found that their political positions could
be exactly described by two quite common English verbs, which differ
only in this, that the one is longer by one letter than the other, while
the rest of the letters are the same, and in the same order. What are
these two verbs?
A PRIZE REBUS
55. The following is a prize Rebus:--
done |
mutt | a glutt
and |
i | T. c. d.
you make me
A LETTER TANGLE
56. First a _c_ and _a_ _t_, last _a_ _c_ and a _t_,
With a couple of letters between,
Form a sight that our eyes are delighted to see,
Unless in their sight it is seen.
A TRANSPOSITION
57. Cut off my tail and set it at my head,
What was an island is a little bear instead.
A REBUS
T S.
58. What English word do these two letters indicate? There are two
possible solutions of equal merit.
A PHONETIC PHRASE
59. How can we read this?
I N X I N X I N.
A GOOD END
60.
[Illustration: I F S]
SOLUTIONS
CHESS CAMEOS
No. XXVI
Black has made the false move Kt from Q sq to Kt 3. When this is
replaced, and the king is moved as the proper penalty, White mates at
once with one or other of the Knights.
No. XXVII
Replace the White Kt at B 7, and a Black Pawn at K 4; then P takes P _en
pas_. Mate.
ANALYSIS AND PROOF
It can be proved that Black’s last move _must have been_ P from K 2 to K
4, so that White may take the P _en pas_.
The Black King cannot have moved from any _occupied_ square.
(The White Kt now occupies B 7.)
Nor from Kt 3 or 4, as both are now _doubly_ guarded, so that he cannot
have moved _out of a check_.
(The White Kt now helps to guard Kt 5.)
Nor can he have moved from K 2, as the White P on Q 6 cannot have moved
_to give check_.
No other P can have moved.
The K P cannot have moved from K 3, became of the position of the White
King.
Therefore Black’s last move _must have been_ P from K 2 to K 4, which
White can take _en pas_ giving Mate.
No. XXVIII
B--Q 2 B--R 5 P--Kt 4
-------- ---------------- ------- White has no move.
P--R 7 P--R 7 becomes Q any
The way in which the B runs to earth and is shut in is most ingenious.
Black with the new Q cannot anyhow give White a move.
No. XXIX
R--Kt 7, ch. R--Kt 5 R--B 5, ch.
------------ ----------- -----------------
K moves P becomes Q Q × R, stalemate.
No. XXX
B--Kt 8.
No. XXXI
B--R 4.
No. XXXII
B--R sq.
No. XXXIII
B--Q 4.
No. XXXIV
B--B sq.
No. XXXV
K--R 4.
No. XXXVI
Kt--Kt’s 6.
No. XXXVII
R--Kt 5 Kt--B 6 Kt × Kt mate.
------- ----------- -------------
Kt × R Kt--B 6 ch.
No. XXXVIII
Kt--R 7 Q--KB 8 Q--R 8 mate.
------- --------- ------------
B moves B returns
Any other move of the Kt would impede the movements of the Q.
No. XXXIX
R--R sq. Q--Kt sq. Q to Kt sq. mate.
-------- ---------- -----------------
B moves. B returns.
No. XL
This beautiful problem is solved by:--
Q--Kt 6 K--B 2 mates accordingly.
------- ------ ------------------
P × Q any
or
R--B 3 mates accordingly.
------- ------ ------------------
Kt--K 3 any
No. XLI
R--R 2. Q--R sq. Q mates.
------- -------- --------
B × Kt any
if
Kt--QB 8, Q or Kt mates.
-------- --------- --------------
B--Q sq. any
if
Kt--QB 6, Q or Kt mates.
----------- --------- --------------
B elsewhere any
No. XLII
Kt--Kt 4, dis. ch. Q--KR 2, ch. Kt--B 2, mate.
------------------ ------------ --------------
K--R 8. P × Q.
There are other variations.
No. XLIII
B--Kt sq. Q--QR 7, Q mates.
--------- -------- --------
P × Kt, K × Kt.
If K × Kt, Q × P, and mates next move.
No. XLIV
K--Q 7, R--Q 5, Q mates.
------- ------- --------
K moves K × R
No. XLV
R--Q 8 Q × P, ch. B mates.
------- ---------- --------
K moves K × Q
if
Q--K 7 Q mates.
------- ------ --------
B moves any
No. XLVI
B--B 6 Q--Q 7, ch. R mates.
------ ----------- --------
K × R K × Q
if
R--B 6, ch. Q mates.
----- ----------- --------
B × R K × P
There are other variations.
No. XLVII
Q--R 8 Kt--B 6 mates accordingly.
------ ------- ------------------
Kt × Q any
No. XLVIII
B--Kt 8 Q × B, ch. Q--QR 7, mate.
--------- ---------- --------------
B--K Kt 2 Kt--K 4
if
Q--Q 2, ch. P mates.
------ ----------- --------
B--B 3 K moves
No. XLIX
B-Kt 2 Q--K 3 ch. mates.
------ ---------- ------
K--K 4 any
There are other variations.
No. L
Q--KR 2 Q--Q 6, ch. Kt--K 5. double ch. mate.
------------- ----------- -------------------------
K--B 3 or B 4 Q × Q
There are other variations.
No. LI
R--QR sq. R--R 2 P mates.
--------- ------ --------
P moves P × R
No. LII
Q--B sq. Q × BP ch. Q mates.
-------- ---------- --------
P--K 7 K--Q 3
if
Q × BP ch. Q mates.
------ ---------- --------
K--Q 2 K--B 3
There are other variations.
No. LIII
B--R 8 Q--QR sq. Q--QKt. 7, mate.
------ --------- ----------------
K--R 2 K moves
No. LIV
Q--R 5 Kt--Kt 5 Kt mates.
--------------- -------- ---------
B × Q or B--B 2 any
No. LV
K--Kt 7 Q--Q 5, ch. Kt. mates.
------- ----------- ----------
Kt--B 3 Kt × Q
if
Q--B 8, ch. Q mates.
------- ------- --------
P--K 3 K moves
No. LVI
R--Kt 6 B--Kt 4 R × P mate.
------- ------- -----------
P moves P × B
No. LVII
Kt from R 3--Kt 5 B--B 4 P--Q 4 ch. R--B 5 mate.
----------------- ------ -------------- ------------
P × Kt P × B P × P _en pas_
if
R--Kt 5 ch. mates accordingly.
----- ----------- ------------------
R × B any
and if
Kt--Q 6 R--B 5 ch. Kt--B 7 mate.
------ ------- ---------- -------------
Q--K 6 Q--Kt 3 Q × R
SCIENCE AT PLAY
No. LVIII.--THE GEARED WHEELS
The arrow head at the top of a small wheel with ten teeth, which is
geared into and revolved round a large fixed wheel with forty teeth,
will point directly upwards five times in its course round the large
wheel. Four of these turnings are due to the rotation of the small wheel
on its own axis, and one of them results from its revolution round the
large wheel.
No. LX.--THE FIFTEEN BRIDGES
It is possible to pass over all the bridges which connect the islands
_A_ and _B_ and the banks of the surrounding river without going over
any of them twice.
The course can be shown thus, using capital letters for the different
regions of land, and italics for the bridges:--E_a_ F_b_ B_c_ F_d_ A_e_
F_f_ C_g_ A_h_ C_i_ D_k_ A_m_ E_n_ A_p_ B_q_ E_l_D.
This order of the bridges can, of course, be reversed.
No. LXVI.--A DUCK HUNT
In order that a spaniel starting from the middle of a circular pond, and
going at the same pace as a duck that is swimming round its edge, shall
be sure to catch it speedily, the dog must always keep in the straight
line between the duck and the centre of the pond.
The duck can never gain an advantage by turning back, and if it swims on
continuously in a circle it will be overtaken when it has passed through
a quarter of the circumference, for the dog will in the same time have
described a semi-circle whose diameter is the radius of the pond, ending
at the point where the duck is caught.
No. LXIX.--THE TETHERED BIRD
When a bird tethered by a cord 50 feet long to a post 6 inches in
diameter uncoils the full length of the cord, and recoils it in the
opposite direction, keeping it always taut, it flies 10,157 feet, or
very nearly 2 miles, in its double course.
To avoid possible misunderstanding, we point out that, in order to pass
from the uncoiling to the recoiling position, the bird must fly through
a semicircle at the end of the fully extended cord.
No. LXX.--THE MOVING DISC AND THE FLY
[Illustration]
When a fly, starting from the point _A_, just outside the revolving
disc, and always making straight for its mate at the point _B_, crosses
the disc in four minutes, during which time the disc is turning twice,
the revolution of the disc has a most curious and interesting effect on
the path of the fly.
The fly is a quarter of a minute in passing from the outside circle to
the next, during which the disc has made an eighth of a revolution, and
the fly has reached the point marked 1. The succeeding points up to 16
show the position of the fly at each quarter of a minute, until, by a
prettily repeated curve, _B_ is reached.
No. LXXI.--A SHUNTING PUZZLE
The following method enables the engine _R_ to interchange the positions
of the wagons, _P_ and _Q_, for either of which there is room on the
straight rails at _A_, while there is not room there for the engine,
which, if it runs up either siding, must return the same way:--
1. _R_ pushes _P_ into _A_. 2. _R_ returns, pushes _Q_ up to _P_ in _A_,
couples _Q_ to _P_, draws them both out to _F_, and then pushes them to
_E_. 3. _P_ is now uncoupled, _R_ takes _Q_ back to _A_, and leaves it
there. 4. _R_ returns to _P_, pulls _P_ back to _C_, and leaves it
there. 5. _R_, running successively through _F_, _D_, _B_, comes to _A_,
draws _Q_ out, and leaves it at _B._
No. LXXV.--PHARAOH’S SEAL
It is quite puzzling to decide how many similar triangles or pyramids
are expressed on the seal of Pharaoh. There are in fact 96.
No. LXXVI.--ROUND THE GARDEN
The four persons who started at noon from the central fountain, and
walked round the four paths at the rates of two, three, four, and five
miles an hour would meet for the third time at their starting point at
one o’clock, if the distance on each track was one-third of a mile.
No. LXXVII.--A JOINER’S PUZZLE
This diagram shows how to divide Fig. _A_ into two parts, and so
rearrange these that they form either Fig. _B_ or Fig. _C_, without
turning either of the pieces.
+--------------+
| |
+--------------+ | +--+
| | | |
| +--+ +--------------+--+ | +--+
| | | | | | | | |
| +--+ | | +--+ | | +--+ |
| | | | | | | | |
| +--+ | | +--+ | | +--+ |
| | | | | | | | |
| +--+ | | +--+ | +--+ |
| | | | | | | |
+--+ | | +--+ | +--+ |
| | | | | | |
+--------------+ +--+--------------+ +--------------+
A B C
Cut the five steps, and shift the two pieces as is shown.
No. LXXVIII.--THE BROKEN OCTAGON
The Broken Octagon is repaired and made perfect if its pieces are put
together thus:--
[Illustration]
No. LXXIX.--AT A DUCK POND
The pond was doubled in size without disturbing the duck-houses, thus:--
+-----------○-----------+
| / \ |
| / \ |
| / \ |
| / \ |
| / \ |
○ ○
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
+-----------○-----------+
No. LXXX.--ALL ON THE SQUARE
This is a perfect arrangement:--
[Illustration]
No. LXXXI.--PINS AND DOTS
The pins may be placed thus:--
On the third dot in the top line; on the sixth dot in the second line;
on the second dot in the third line; on the fifth dot in the fourth
line; on the first dot in the fifth line; on the fourth dot in the sixth
line.
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
| \ / | \ / | \ / | \ / | \ / |
| \ / | \ / | \ / | \ / | \ / |
| * | * | * | * | * |
| / \ | / \ | / \ | / \ | / \ |
| / \ | / \ | / \ | / \ | / \ |
*-----------*-----------*-----------*-----------*-----------*
No. LXXXII.--A TRICKY COURSE
To trace this course draw lines upon the diagram from square 46 to
squares 38, 52, 55, 23, 58, 64, 8, 57, 1, 7, 42, 10, 13, 27, and 19.
This gives fifteen lines which pass through every square only once.
No. LXXXIII.--FOR THE CHILDREN
Make a square with three on every side, and place the remaining four one
on each of the corner men or buttons.
No. LXXXVII.--LOYD’S MITRE PROBLEM
The figure given is thus divided into four equal and similar parts:--
[Illustration]
No. LXXXIX.--CUT OFF THE CORNERS
A E F B
+------+--------+------+
| / \ |
| / \ |
|/ \|
M+ +G
| |
| |
| |
L+ +H
|\ /|
| \ / |
| \ / |
+------+--------+------+
C K I D
A very simple rule of thumb method for striking the points in the sides
of a square, which will be at the angles of an octagon formed by
cutting off equal corners of the square, is to place another square of
equal size upon the original one, so that the centre is common to both,
and the diagonal of the new square lies upon a diameter of the other
parallel to its side.
No. XCIII.--MAKING MANY SQUARES
The subjoined diagram shows how the two oblongs, applied to the two
concentric squares, produce 31 perfect squares, namely, 17 small ones,
one equal to 25 of these, 5 equal to 9, and 8 equal to 4.
+------+
| |
| |
+-------------+------+-------------+
| | | |
| | | |
| +------+------+------+ |
| | | | | |
| | | | | |
+-----+------+------+------+------+------+------+
| | | | | | | |
| | | | | | | |
+-----+------+------+------+------+------+------+
| | | | | |
| | | | | |
| +------+------+------+ |
| | | |
| | | |
+-------------+------+-------------+
| |
| |
+------+
No. XCIV.--CUT ACROSS
The Greek Cross can be divided by two straight cuts, so that the
resulting pieces will form a perfect square when re-set, as is shown in
these figures:--
[Illustration]
No. CV.--A TRANSFORMATION
The diagram which is given below shows how the irregular Maltese Cross
can be divided by two straight cuts into four pieces, which form when
properly rearranged, a perfect square.
[Illustration]
No. CVI.--SHIFTING THE CELLS
The following diagram shows by its dark lines how the whole square can
be cut into four pieces, and these arranged as two perfect squares in
which every semicircle still occupies the upper half of its cell.
One piece forms a square of nine cells, and it is easy to arrange the
other three pieces in a square of sixteen cells by lifting the three
cells and dropping the two.
+-----------+-----------+-----------+-----------+-----------+
| / \ | / \ | / \ | / \ ∥ / \ |
| / \ | / \ | / \ | / \ ∥ / \ |
|/ \|/ \|/ \|/ \∥/ \|
| | | | ∥ |
| | | | ∥ |
+-----------+-----------+-----------+-----------+-----------+
| / \ | / \ | / \ | / \ ∥ / \ |
| / \ | / \ | / \ | / \ ∥ / \ |
|/ \|/ \|/ \|/ \∥/ \|
| | | | ∥ |
| | | | ∥ |
+-----------+-----------+===========+===========+===========+
| / \ | / \ ∥ / \ | / \ | / \ |
| / \ | / \ ∥ / \ | / \ | / \ |
|/ \|/ \∥/ \|/ \|/ \|
| | ∥ | | |
| | ∥ | | |
+-----------+===========+-----------+-----------+-----------+
| / \ ∥ / \ ∥ / \ | / \ | / \ |
| / \ ∥ / \ ∥ / \ | / \ | / \ |
|/ \∥/ \∥/ \|/ \|/ \|
| ∥ ∥ | | |
| ∥ ∥ | | |
+===========+-----------+-----------+-----------+-----------+
| / \ | / \ ∥ / \ | / \ | / \ |
| / \ | / \ ∥ / \ | / \ | / \ |
|/ \|/ \∥/ \|/ \|/ \|
| | ∥ | | |
| | ∥ | | |
+-----------+-----------+-----------+-----------+-----------+
No. CVII.--IN A TANGLE
[Illustration]
It will be seen, on the subjoined diagram, how twenty-one counters or
coins can be placed on the figure so that they fall into symmetrical
design, and form thirty rows, with three in each row.
No. CVIII.--STILL A SQUARE
A
+------+------+------+
| | | |
| | | |
+------+------+------+ C
| | |
| | |
+------+------+
B
In order that a square and an additional quarter may be divided by two
straight lines so that their parts, separated and then reunited, form a
perfect square, lines must be drawn from the point _A_ to the corners
_B_ and _C_. Draw the figure on paper, cut through these lines, and you
will find that the pieces can be so reunited that they form a perfect
square.
No. CIX.--A TRANSFORMATION
The diagram below shows how the seven parts of the square can be
rearranged so that they form the figure 8.
[Illustration]
No. CX.--TO MAKE AN OBLONG
Here is an oblong formed by piecing together two of the smaller
triangles, and four of each of the other patterns--
[Illustration]
Here is another:--
[Illustration]
No. CXI.--SQUARES ON THE CROSS
This diagram shows how every indication of the seventeen squares is
broken up by the removal of seven of the asterisks which mark their
corners.
[Illustration]
Those surrounded by circles are to be removed.
No. CXII.--A CHINESE PUZZLE
|\
| \
| \
| \
| \
| \
| +--\
| | \
| +--+--+ \
| | | \
| +--+ +--+\
| | | \
+--+ +--+\
| | \
+-----------------+--+
The dotted lines on the triangular figure show how a piece of cardboard
cut to the shape of Fig. 1 can be divided into three pieces, and
rearranged so that these form a star shaped as in Fig. 2.
No. CXIII.--FIRESIDE FUN
To solve this puzzle slip the first coin or counter from _A_ to _D_,
then the others in turn from _F_ to _A_, from _C_ to _F_, from _H_ to
_C_, from _E_ to _H_, from _B_ to _E_, from _G_ to _B_, and place the
last on _G_. It can only be done by a sequence of this sort, in which
each starting point is the finish of the next move.
[Illustration]
AMUSING PROBLEMS
1. THE CARPENTER’S PUZZLE
The carpenter cleverly contrived to mend a hole 2 feet wide and 12 feet
long, by cutting the board which was 3 feet wide and 8 feet long, as is
shown in Fig. 1, and putting the two pieces together as is shown in Fig.
2.
Fig. 1.
+----------------+
| ________|
|________| |
| |
+----------------+
Fig. 2.
+------------------------+
| ________¦ |
| ¦ |
+------------------------+
2. GOLDEN PIPPINS
Here is another solution:--
1| 3| 5| 7| 9|11|13|15|17|19
39|37|35|33|31|29|27|25|23|21
2| 4| 6| 8|10|12|14|16|18|20
40|38|36|34|32|30|28|26|24|22
--+--+--+--+--+--+--+--+--+--
82|82|82|82|82|82|82|82|82|82
3. AN AWKWARD FIX
I was able to find my way in a strange district, when the sign-post lay
uprooted in the ditch, without any difficulty. I simply replaced the
post in its hole, so that the proper arm, with its lettering, _pointed
the way that I had come_, and then, of necessity, the directions of the
other arms were correct.
4. LINKED SWEETNESS LONG DRAWN OUT
The train was whistling for 5 minutes. Sound travels about a mile in 5
seconds, so the first I heard of it was 5 seconds after it began. Its
last sound reached me 7¹⁄₂ seconds after it ceased, so I heard the
whistle for 5 minutes, 2¹⁄₂ seconds.
5. These quarters were not so elastic as they are made to appear. In
good truth, considering that the second man who was placed in _A_ was
afterwards removed to _I_, no real _second_ man was provided for at
all.
6. The first day of a new century can never be Sunday, Wednesday, or
Friday. The cycle of the Gregorian calendar is completed in 400 years,
after which all dates repeat themselves.
As in this cycle there are only four first days of a century, it is
clear that three of the seven days of the week must be excluded. Any
perpetual calendar shows that the four which do occur are Monday,
Tuesday, Thursday, and Saturday, so that Sunday, Wednesday, and Friday
are shut out.
A neat corollary to this proof is that Monday is the only day which may
be the first, or which may be the last, day of a century.
7. A cricket bat with spliced handle has such good driving power,
because the elasticity of the handle allows the ball to be in contact
with the blade of the bat for a longer time than would otherwise be
possible.
With similar effect the “follow through” of the club head at golf
maintains contact with the ball, when it is already travelling fast.
8. When two volumes stand in proper order on my bookshelf, each 2 inches
thick over all, with covers ¹⁄₈ of an inch in thickness, a bookworm
would only have to bore ¹⁄₄ of an inch, to penetrate from the first page
of Vol. I, to the last page of Vol. II, for these pages would be in
actual contact if there was no binding. This very pretty and puzzling
question combines in its solution all the best qualities of a clever
catch with solid and simple facts.
9. A man would have to fall from a height of nearly 15 miles to reach
earth before the sound of his cry as he started. The velocity of sound
is constant, while that of a falling body is continually accelerated. At
first the cry far outstrips the falling man, but he _overtakes and
passes through his own scream_ in about 14¹⁄₂ miles, for his body falls
through the 15 miles in 70 seconds, and sound travels as far in 72
seconds. Air resistance, and the fact that sound cannot pass from a rare
to a dense atmosphere, are disregarded in this curious calculation.
10. A man on a perfectly smooth table in a vacuum, and where there was
no friction, though no contortions of his body would avail to get away
from this position, could escape from the predicament by throwing from
him something which he could detach from his person, such as his watch
or coat. He would himself instantly slide off in the opposite direction!
11. The monkey clinging to one end of a rope that passes over a single
fixed pulley, while an equal weight hangs on the other end, cannot climb
up the rope, or rise any higher from the ground.
If he continues to try to climb up, he will gradually pull the balancing
weight on the other end of the rope upwards, and the slack of the rope
will drop below him, while he remains in the same place.
If, after some efforts, he rests, he will sink lower and lower, until
the weight reaches the pulley, because of the extra weight of rope on
his side, if friction is disregarded.
12. Though the tension on a pair of traces tends as much to pull the
horse backward as it does to pull the carriage forward, it is the
initial pull from slack to taut which sets the traces in motion; and
this, once started, must continue indefinitely until checked by a
counter pull.
13. Some say that a rubber tyre leaves a double rut in dust and a
single one in mud, because the air, rushing from each side into the wake
of the wheel, piles up the loose dust. Others hold that the central
ridge is caused by the continuous contraction of the tyre as it passes
its point of contact with the road.
A correspondent, writing some years ago to “Knowledge,” said:--“It is
our old friend the sucker. The tyre being round, the weight on centre of
track only is great enough to enable the tyre to draw up a ridge of dust
after it.”
14. If two cats on a sloping roof are on the point of slipping off, one
might think that whichever had the longest paws (pause) would hold on
best. Todhunter, in playful mood, saw deeper into it than that, and
pronounced for the cat that had the _highest mew_, for to his
mathematical mind the Greek letter _mu_ was the coefficient of friction!
15. If a penny held between finger and thumb, and released by
withdrawing the finger, starts “heads” and makes half a turn in falling
through the first foot, it will be “heads” again on reaching the floor,
if it is held four feet above it at first.
16. HE DID IT!
Funnyboy had secretly prepared himself for the occasion by rubbing the
chemical coating from the side of the box on to his boot.
17. THE CYCLE SURPRISE
If a bicycle is stationary, with one pedal at its lowest point, and that
pedal is pulled backwards, while the bicycle is lightly supported, the
bicycle will move backwards, and the pedal relatively to the bicycle,
will move forwards. This would be quite unexpected by most people, and
it is well worth trying.
18. The rough stones, by which any number of pounds, from 1 to 364, can
be weighed, are respectively 1 ℔., 3 ℔s., 9 ℔s., 27 ℔s., 81 ℔s., and 243
℔s. in weight.
19. If we disregard the resistance of the air, a small clot of mud
thrown from the hindermost part of a wheel would describe a parabola,
which would, in its descending limb, bring it back into kissing contact
with the wheel which had rejected it.
20. THE CARELESS CARPENTER
When the carpenter cut the door _too little_, he did not in fact _cut it
enough_, and he had to cut it again, so that it might fit.
21. If from the North Pole you start sailing in a south-westerly
direction, and keep a straight course for twenty miles, you must steer
due north to get back as quickly as possible to the Pole, if, indeed, it
has been possible to start from it in any direction other than due
south.
22. DICK IN A SWING
Dick’s feet will travel in round numbers nearly 16 feet further than his
head, or to be exact, 15·707,960 feet.
23. A POSER
The initial letters of Turkey, Holland, England, France, Italy, Norway,
Austria, Lapland, and Spain spell, and in this sense are the same as,
“the finals.”
CURIOUS CALCULATIONS
1. The only sum of money which satisfies the condition that its pounds,
shillings, and pence written down as a continuous number, exactly give
the number of farthings which it represents, is £12, 12s., 8d., for this
sum contains 12,128 farthings.
2. If, when a train, on a level track, and running all the time at 30
miles an hour, slips a carriage which is uniformly retarded by brakes,
and this comes to rest in 200 yards, the train itself will then have
travelled 400 yards.
The slip carriage, uniformly retarded from 30 miles an hour to no miles
an hour, has an average speed of 15 miles an hour, while the train
itself, running on at 30 miles an hour all the time, has just double
that speed, and so covers just twice the distance.
3. The traveller had fivepence farthing when he said to the landlord,
“Give me as much as I have in my hand, and I will spend sixpence with
you.” After repeating this process twice he had no money left.
4. This is the way to obtain eleven by adding one-third of twelve to
four-fifths of seven--
TW(EL)VE + S(EVEN) = ELEVEN
5. Here is the completed sum:--
215)*7*9*(1** 215)37195(173
*** 215
---- ----
*5*9 1569
*5*5 1505
---- ----
*4* 645
*** 645
=== ===
The clue is that no figure but 3, when multiplied into 215, produces 4
in the tens place.
6. If I attempt to buy as many heads of asparagus as can be encircled by
a string 2 feet long for double the price paid for as many as half that
length will encompass, I shall not succeed. A circle double of another
in circumference is also double in diameter, and its area is four times
that of the other.
7. If, when you reverse me, and my square, and my cube, and my fourth
power, you find that no changes have been made, I am 11, my square is
121, my cube 1331, and my fourth power 14641.
8. A thousand pounds can be stored in ten sealed bags, so that any sum
in pounds up to £1,000 can be paid without breaking any of the seals, by
placing in the bags 1, 2, 4, 8, 16, 32, 64, 128, 256, and 489
sovereigns.
9. It is the fraction ⁶⁄₉ which is unchanged when turned over, and
which, when taken thrice, and then divided by two becomes 1.
10. When the three gamblers agreed that the loser should always double
the sum of money that the other two had before them, and they each lost
once, and fulfilled the conditions, remaining each with eight sovereigns
in hand, they had started with £13, £7, and £4 as the following table
shows:--
A B C
£ £ £
At starts 13 7 4
When A loses 2 14 8
When B loses 4 4 16
When C loses 8 8 8
11. Tom’s sum, which his mischievous neighbour rubbed almost out, is
reconstructed thus:--
345 345
** 37
----- -----
**** 2415
**** 1035
----- -----
**76* 12765
12. Here are two other arrangements of the nine digits which produce 45,
their sum; each is used once only:--
5 × 8 × 9 × (7 + 2)
------------------- = 45
1 × 3 × 4 × 6
7² - 5 × 8 × 9
-------------- + 1 = 45
3 × 4 × 6
13. If, when the combined ages of Mary and Ann are 44, Mary is twice as
old as Ann was when Mary was half as old as Ann will be when Ann is
three times as old as Mary was when Mary was three times as old as Ann,
Mary is 27¹⁄₂ years old, and Ann is 16¹⁄₂.
For, tracing the question backwards, when Ann was 5¹⁄₂ Mary was 16¹⁄₂.
When Ann is three times that age she will be 49¹⁄₂. The half of this is
24³⁄₄, and when Mary was at that age Ann was 13³⁄₄. Mary’s age, by the
question, was twice this, or 27¹⁄₂.
14. It is safer at backgammon to leave a blot in the tables which can be
taken by an ace than one which a three would hit. In either the case of
an actual ace or a three the chance is one in eleven; but there are two
chances of throwing deuce-ace, the equivalent of three.
15. If I start from a bay, where the needle points due north, 1200 miles
from the North Pole, and the course is perfectly clear, I can never
reach it if I steam continuously 20 miles an hour, steering always north
by the compass needle. After about 200 miles I come upon the Magnetic
Pole, which so affects the needle that it no longer leads me northward,
and I may have to steer south by it to reach the geographical Pole.
16. The 21 casks, 7 full, 7 half full, and 7 empty, were shared equally
by A, B, and C, as follows:--
Full cask. Half full. Empty.
A 2 3 2
B 2 3 2
C 3 1 3
or--
A 3 1 3
B 3 1 3
C 1 5 1
Thus each had 7 casks, and the equivalent of 3¹⁄₂ caskfuls of wine.
17. The foraging mouse, able to carry home three ears at a time from a
box full of ears of corn, could not add more than fourteen ears of corn
to its store in fourteen journeys, for it had each time to carry along
two ears of its own.
18. If, with equal quantities of butter and lard, a small piece of
butter is taken and mixed into all the lard, and if then a piece of this
blend of similar size is put back into the butter, there will be in the
end exactly as much lard in the butter as there is butter in the lard.
19. The fallacy of the equation--
4 - 10 = 9 - 15
4 - 10 + ²⁵⁄₄ = 9 - 15 + ²⁵⁄₄
and the square roots of these--
2 - ⁵⁄₂ = 3 - ⁵⁄₂
therefore 2 = 3
is explained thus:--The fallacy lies in ignoring the fact that the
square roots are _plus or minus_. In the working we have taken both
roots as _plus_. If we take one root plus, and the other minus, and add
⁵⁄₂, we have either 2 = 2, or 3 = 3.
20. The largest possible parcel which can be sent through the post under
the official limits of 3 feet 6 inches in length, and 6 feet in length
and girth combined, is a cylinder 2 feet long and 4 feet in
circumference, the cubic contents of which are 2⁶⁄₁₁ cubic feet.
21. We can show, or seem to show, that either four, five, or six nines
amount to 100, thus:--
IX
IX
99⁹⁄₉ = 100 IX 9 × 9 + 9 + 9⁹⁄₉ = 100
IX
IX
---
100
22. This is the magic square arrangement, so contrived that the
products of the rows, columns, and diagonals are all 1,000.
+---+---+---+
| 50| 1| 20|
+---+---+---+
| 4| 10| 25|
+---+---+---+
| 5|100| 2|
+---+---+---+
23. If seven boys caught four crabs in the rock-pools at Beachy Head in
six days, the twenty-one boys who searched under the seaweed and only
caught one crab with the same rate of success were only at work for
_half a day_.
24. A watch could be set of a different trio from a company of fifteen
soldiers for 455 nights, and one of them, John Pipeclay, could be
included ninety-one times.
25. If Augustus Cæsar was born September 23, B.C. 63, he celebrated his
sixty-third birthday on September 23, B.C. 0; or, writing it otherwise,
September 23, A.D. 0; or again, if we wish to include both symbols, B.C.
0 A.D. It is clear that his sixty-second birthday fell on September 23,
B.C. 1, and his sixty-fourth on September 23, A.D. 1, so that the
intervening year may be written as above.
26. The difference of the ages of _A_ and _B_ who were born in 1847 and
1874, is 27, or 30 - 03. Hence, when _A_ was 30 _B_ was 03. And _A_ was
30 in 1877. Eleven years later _A_ was 41 and _B_ 14, and eleven years
after that _A_ was 52 and _B_ 25. Thus the same two digits served to
express the ages of both in 1877, 1888, and 1899. This can only happen
in the cases of those whose ages differ by some multiple of nine.
27 A hundred and one by fifty divide,
To this let a cypher be duly applied;
And when the result you can rightly divine,
You find that its value is just one in nine--
is solved by CLIO, one of the nine Muses.
28. The man who paid a penny on Monday morning to cross the ferry, spent
half of what money he then had left in the town, and paid another penny
to recross the ferry, and who repeated this course on each succeeding
day, reaching home on Saturday evening with one penny in his pocket,
started on Monday with £1 1s. 1d. in hand.
29. When the three men agreed to share their mangoes equally after
giving one to the monkey, and when each helped himself to a third after
giving one to the monkey, without knowing that anyone had been before
him, and they finally met together, gave one to the monkey, and divided
what still remained, there must have been at least seventy-nine mangoes
for division at the first.
30. If, after having looked at my watch between 4 and 5, I look again
between 7 and 8, and find that the hour and minute-hands have then
exactly changed places, it was 36 12-13 minutes past 4 when I first
looked. At that time the hour-hand would be pointing to 23 1-13 minutes
on the dial, and at 23 1-13 minutes past 7 the hour hand would be
pointing to 36 12-13 minutes.
31. The number consisting of 22 figures, of which the last is 7, which
is increased exactly sevenfold if this 7 is moved to the first place, is
1,014,492,753,623,188,405,797.
32. The two sacks of wheat, each 4 feet long and 3 feet in
circumference, which the farmer sent to the miller in repayment for one
sack 4 feet long and 6 feet in circumference, far from being a
satisfactory equivalent, contained but half the quantity of the larger
sack, for the area of a circle the diameter of which is double that of
another is equal to four times the area of that other.
33. The five gamblers, who made the condition that each on losing should
pay to the others as much as they then had in hand, and who each lost in
turn, and had each £32 in hand at the finish, started with £81, £41,
£21, £11, and £6 respectively.
34. If we know the square of any number, we can rapidly determine the
square of the next number, without multiplication, by adding the two
numbers to the known square. Thus if we know that the square of 87 is
7569,
then the square of 88 = 7569 + 87 + 88 = 7744;
so too the square of 89 = 7744 + 88 + 89 = 7921;
and the square of 90 = 7921 + 89 + 90 = 8100.
35. The two numbers which solve the problem--
Two numbers seek which make eleven,
Divide the larger by the less,
The quotient is exactly seven,
As all who find them will confess--
are 1³⁄₈ and 9⁵⁄₈, for 1³⁄₈ + 9⁵⁄₈ = 11, and ⁷⁷⁄₈ ÷ ¹¹⁄₈ = 7.
36. There must be nine things of each sort, in order that
^99999999999999999999^ different selections may be made from twenty
sorts of things.
37. The women who had respectively 33, 29, and 27 apples, and sold the
same number for a penny, receiving an equal amount of money, began by
selling at the rate of three a penny. The first sold ten pennyworth, the
second eight pennyworth, and the third seven pennyworth.
The first had then left three apples, the second five, and the third
six. These they sold at one penny each, so that they received on the
whole--
The first 10d. + 3d. = 13d.
The second 8d. + 5d. = 13d.
The third 7d. + 6d. = 13d.
38. The puzzle--
Take five from five, oh, that is mean!
Take five from seven, and this is seen--
is solved by _fie_, _seen_.
39. If a bun and a half cost three halfpence, it is plain that each bun
costs a penny, but, by general custom, you buy seven for sixpence.
40. The hands of a watch would meet each other twenty-five times in a
day, if the minute-hand moved backwards and the hour-hand forwards. They
are, of course, together at starting.
41. The only way in which half-a-crown can be equally divided between
two fathers and two sons, so that a penny is the smallest coin made use
of, is to give tenpence each to a grandfather, his son, and his
grandson.
42. If the number of the revolutions of a bicycle wheel in six seconds
is equal to the number of miles an hour at which it is running, the
circumference of the wheel is 8⁴⁄₅ feet.
43. The hour that struck was twelve o’clock.
44. Sixty years.
45. If I jump off a table with a 20lb dumb-bell in my hand there is no
pressure upon me from its weight while I am in the air.
46. If at a bazaar I paid a shilling on entering each of four tents, and
another shilling on leaving it, and spent in each tent half of what was
in my pocket, and if my fourth payment on leaving took my last shilling,
I started with 45s., spending 22s. in tent 1, 10s. in tent 2, 4s. in
tent 3, and 1s. in tent 4, having also paid to the doorkeepers 8s.
47. When rain is falling vertically at 5 miles an hour, and I am walking
through it at 4 miles an hour, the rain drops will strike the top of my
umbrella at right angles if I hold it at an angle of nearly 39 degrees.
As I walk along, meeting the rain, the effect is the same as it would be
if I was standing still, and the wind was blowing the rain towards me at
the rate of 4 miles an hour.
48. When one monkey descends from the top of a tree 100 cubits high, and
makes its way to a well 200 yards distant, while another monkey, leaping
upwards from the top, descends by the hypotenuse to the well, both
passing over an equal space, the second monkey springs 50 cubits into
the air.
49. The steamboat which springs a leak 105 miles east of Tynemouth
Lighthouse, and, putting back, goes at the rate of 10 miles an hour the
first hour, but loses ground to the extent in each succeeding hour of
one-tenth of her speed in the previous hour, never reaches the
lighthouse, but goes down 5 miles short of it.
50. Twenty-one hens will lay ninety-eight eggs in a week, if a hen and
a-half lays an egg and a-half in a day and a-half. Evidently one egg is
laid in a day by a hen and a-half, that is to say three hens lay two
eggs in a day. Therefore, twenty-one hens lay fourteen eggs, in a day,
or ninety-eight in a week.
Q. E. D. (Quite easily done!)
51. If the population of Bristol exceeds by 237 the number of hairs on
the head of anyone of its inhabitants that are not bald, at least 474 of
them must have the same number of hairs on their heads.
52. In tipping his nephew from seven different coins, the uncle may give
or retain each, thus disposing of it in two ways, or of all in 2 × 2 × 2
× 2 × 2 × 2 × 2 ways. But as one of these ways would be to retain them
all, there are not 128, but only 127 possible variations of the tip.
53. The prime number which fulfils the various conditions of the
question is 127. Increased by one-third, excluding fractions, it becomes
169, the square of 13. If its first two figures are transposed, and it
is increased by one-third, it becomes 289, the square of 17. If its
first figure is put last, and it is increased by one-third, it becomes
361, the square of 19. If, finally, its three figures are transposed,
and then increased by one-third, it becomes 961, the square of 31.
54. Six things can be divided between two boys in 62 ways. They could be
_carried_ by two boys in 64 ways (2 × 2 × 2 × 2 × 2 × 2), but they are
not _divided_ between two boys if all are given to one, so that two of
the 64 ways must be rejected.
55. The highest possible score that the dealer can make at six cribbage,
if he is allowed to select the cards, and to determine the order of
play, is 78. The dealer and his opponent must each hold 3, 3, 4, 4, the
turn-up must be a 5, and crib must have the knave of the suit turned up,
and 5, 5, 5. It will amuse many of our readers to test this with the
cards.
56. The picture frame must be 3 inches in width all round, if it is
exactly to equal in area the picture it contains, which measures 18
inches by 12 inches.
57. If my mother was 20 when I was born, my sister is two years my
junior, and my brother is four years younger still, our ages are 56, 36,
34, and 30.
58. The spider in the dockyard, whose thread was drawn from her by a
revolving capstan 1 foot in diameter, until 73 feet of it were paid out,
after walking for a mile round and round the capstan at the end of the
stretched thread in an effort to unwind it all, had, when she stopped in
her spiral course, 49 more feet to walk to complete her task.
59. The mountebank at a fair, who offered to return any stake a
hundredfold to anyone who could turn up all the sequence in twenty
throws of dice marked each on one face only with 1, 2, 3, 4, 5, or 6,
should in fairness have engaged to return 2332 times the money; for of
the 46,656 possible combinations of the faces of the dice, only one can
give the six marked faces uppermost. Thus the chance of throwing them
all at one throw is expressed by ¹⁄₄₆₆₅₆, and in twenty throws by about
¹⁄₂₃₃₂.
60. If 90 groats (each = 4d.) feed twenty cats for three weeks, and five
cats consume as much as three dogs, seventy-two hounds can be fed for
£39 in a period of ninety-one days.
61. When equal wine-glasses, a half and a third full of wine, are filled
up with water, and their contents are mixed, and one wine-glass is
filled with the mixture, it contains ⁵⁄₁₂ wine and ⁷⁄₁₂ water.
62. The arrangement by which St Peter is said to have secured safety for
the fifteen Christians, when half of the vessel’s passengers were thrown
overboard in a storm, is as follows:--
XXXXIIIIIXXIXXXIXIIXXIIIXIIXXI
Each Christian is represented by an X, and if every ninth man is taken
until fifteen have been selected, no X becomes a victim.
63. If Farmer Southdown’s cow had a fine calf every year, and each of
these, and their calves in their turn, at two years old followed this
example, the result would be no less than 2584 head in sixteen years.
64. The number of the flock was 301. This is found by first taking the
least common multiple of 2, 3, 4, 5, 6, which is 60, and then finding
the lowest multiple of this, which with 1 added is divisible by 7. This
301 is exactly divisible by 7, but by the smaller numbers there is 1 as
remainder.
65. The rule for determining easily the number of round bullets in a
flat pyramid, with a base line of any length, is this:--
Add a half to half the number on the base line, and multiply the result
by the number on that line. Thus, if there are twelve bullets as a
foundation--
12 + ¹⁄₂ = ¹³⁄₂; and ¹³⁄₂ × ¹²⁄₁ = 78.
The same result is reached by multiplying the number on the base line by
a number larger by one, and then halving the result. Thus--
12 × 13 = 156, 156 ÷ 2 = 78.
66. We can gather from the lines--
Old General Host
A battle lost,
And reckoned on a hissing,
When he saw plain
What men were slain,
And prisoners, and missing.
To his dismay
He learned next day
What havoc war had wrought;
He had, at most,
But half his host
Plus ten times three, six, ought.
One-eighth were lain
On beds of pain,
With hundreds six beside;
One-fifth were dead,
Captives, or fled,
Lost in grim warfare’s tide.
Now, if you can,
Tell me, my man,
What troops the general numbered,
When on that night
Before the fight
The deadly cannon slumbered?
that old General Host had an army 24,000 strong.
67. When the farmer sent five pieces of chain of 3 links each, to be
made into one continuous length, agreeing to pay a penny for each link
cut, and a penny for each link joined, the blacksmith, if he worked in
the best interest of the farmer, could only charge sixpence: for he
could cut asunder one set of 3 links, and use these three single links
between the other four sets.
68. If, in a parcel of old silver and copper coins, each silver piece is
worth as many pence as there are copper coins, and each copper coin is
worth as many pence as there are silver coins, there are eighteen silver
and six copper coins, when the whole parcel is worth eighteen shillings.
69. These are five groups that can be arranged with the numbers 1 to 11
inclusive, so that they are all equal:--
(8² - 5² + 1) = (11² - 9²) = (7² - 3²) = (6² + 2²) = 4(10).
70. John Bull, under the conditions given, lived to the age of
eighty-four years.
71. The two numbers to each of which, or to the halves of which, unity
is added, forming in every case a square number, are 48 and 1680.
72. The true weight of a cheese that seemed to weigh 16 ℔s. in one scale
of a balance with arms of unequal length, and only 9℔s. in the other, is
12℔. This is found by multiplying the 16 by the 9, and finding the
square root of the result.
73. The two parts into which 100 can be divided, so that if one of them
is divided by the other the quotient is again exactly 100 are 99¹⁄₁₀₁
and ¹⁰⁰⁄₁₀₁.
74. If, with marbles in two pockets, I add one to those in that on the
right, and then multiply its contents by the number it held at first,
and after dealing in a similar way with those on the left, find the
difference between the two results to be 90; while if I multiply the sum
of the two original quantities by the square of their difference the
result is 176, I started with twenty-three in the right-hand pocket and
twenty-one in the other.
75. The circle of twenty-one friends who arranged to meet each week five
at a time for Bridge so long as exactly the same party did not meet more
than once, and who wished to hire a central room for this purpose, would
need it for no less than 20,349 weeks, or more than 390 years, to carry
out their plan.
76. If a herring and a half costs (not cost) a penny and a half, the
price of a dozen such quantities is eighteenpence.
77. The sum of money which in a sense appears to be the double of itself
is 1s. 10d., for we may write it _one_ and _ten_ pence or _two_ and
_twenty_ pence.
78. The “comic arithmetic” question set by Dr Bulbous Roots--
Divide my fifth by my first, and you have my fourth; subtract my first
from my fifth, and you have my second; multiply my first by my fourth
followed by my second, and you have my third; place my second after my
first, and you have my third multiplied by my fourth--is solved by
COMIC.
79. If the earth could stand still, and a straight tunnel could be bored
through it, a cannon ball dropped into it, if there is no air or other
source of friction, would oscillate continually from end to end.
Taking air into account, the ball would fall short of the opposite end
at its first lap, and in succeeding laps its path would become shorter
and shorter, until its initial energy was exhausted, when it would come
to rest at the centre.
80. He sent 163. She sent 157.
81. When twins were born the estate was properly divided thus:--
Taking the daughter’s share as 1
The widow’s share would be 2
And the son’s share 4
-
Total 7 shares.
So the son takes four-sevenths, the widow two-sevenths, and the daughter
one-seventh of the estate.
82. If each of my strides forwards or backwards across a 22 feet carpet
is 2 feet, and I make a stride every second; and if I take three strides
forwards and two backwards until I cross the carpet, I reach the end of
it in forty-three seconds. In three steps I advance 6 feet. Then in two
steps I retrace 4 feet, thus gaining only 2 feet in five steps, _i.e._,
in five seconds. I therefore advance 16 feet in forty seconds, and three
more strides cover the remaining 6 feet.
83. If the captain of a vessel chartered to sail from Lisbon to New
York, which appear on a map of the world to be on the same parallel of
latitude, and which are, along the parallel, about 3600 miles apart,
takes his ship along this parallel, he will not be doing his best for
the impatient merchant who has had an urgent business call to New York.
The shortest course between the two points is traced by a segment of a
“great circle,” having its centre at the centre of the earth, and
touching the two points. This segment lies wholly north of the parallel,
and is the shortest possible course.
84. When John and Harry, starting from the right angle of a triangular
field, run along its sides, and meet first in the middle of the opposite
side, and again 32 yards from their starting point, if John’s speed is
to Harry’s as 13 to 11, the sides of the field measure 384 yards.
85. If two sorts of wine when mixed in a flagon in equal parts cost
15d., but when mixed so that there are two parts of _A_ to three of _B_
cost 14d., a flagon of _A_ would cost 20d., and a flagon of _B_ 10d.
86. If, when a man met a beggar, he gave him half of his loose cash and
a shilling, and meeting another gave him half what was left and two
shillings, and to a third half the remainder and three shillings, he had
two guineas at first.
87. The clerk who has two offers of work from January 1, one from _A_ of
£100 a year, with an annual rise of £20, and the other from _B_ of £100
a year, with a half-yearly rise of £5, should accept _B_’s offer.
The half-yearly payments from _A_ (allowing for the rise), would be 50,
50, 60, 60, 70, 70, etc., etc.; and from _B_ they would be 50, 55, 60,
65, 70, 75, etc., etc., so that _B_’s offer is worth £5 a year more than
_A_’s always.
88. If I have a number of florins and half-crowns, but no other coins, I
can pay my tailor £11, 10s. in 224 different ways.
This can be found thus by rule of thumb: Start with 0 half-crowns and
115 florins. Then 4 half-crowns and 110 florins. Add 4 half-crowns and
deduct 5 florins each time till 92 half-crowns and 0 florins is reached.
89. The monkey climbing a greased pole, 60 feet high, who ascended 3
feet, and slipped back 2 feet in alternate seconds, reached the top in 1
minute, 55 seconds, for he did not slip back from the top.
90. When Adze, the carpenter, secured his tool-chest with a puzzle lock
of six revolving rings, each engraved with twelve different letters, the
chances against any one discovering the secret word formed by a letter
on each ring was 2,985,983 to 1; for the seventy-two letters may be
placed in 2,985,984 different arrangements, only one of which is the
key.
91. The five married couples who arranged to dine together in
Switzerland at a round table, with the ladies always in the same places,
so long as the men could seat themselves each between two ladies, but
never next to his own wife, were able under these conditions to enjoy
thirteen of these nights at the round table.
92. If in a calm the tip of a rush is 9 inches above the surface of a
lake, and as the wind rises it is gradually blown aslant, until at the
distance of a yard it is submerged, it is growing in water that is 5
feet 7¹⁄₂ inches deep.
93. Aminta was eighteen.
94. When Dick took a quarter of the bag of nuts, and gave the one over
to the parrot, and Tom and Jack and Harry dealt in the same way with the
remainders in their turns, each finding a nut over from the reduced
shares for the bird, and one was again over when they divided the final
remainder equally, there were, at the lowest estimate, 1021 nuts in the
bag.
95. Eight and a quarter is the answer to the nonsense question--
If five times four are thirty-three,
What will the fourth of twenty be?
96. The similar fraction of a pound, a shilling, and a penny which make
up exactly a pound are as follows:--
s. d.
²⁴⁰⁄₂₅₃ of £1 = 18 11¹⁶⁹⁄₂₅₃
²⁴⁰⁄₂₅₃ of 1s. = 11⁹⁷⁄₂₅₃
²⁴⁰⁄₂₅₃ of 1d. = ²⁴⁰⁄₂₅₃
---------------
£1 0 0
========
97. When Dr Tripos thought of a number, added 3, divided by 2, added 8,
multiplied by 2, subtracted 2, and thus arrived at double the number, he
started with 17.
98. When _A_ and _B_ deposited equal stakes with _C_, and agreed that
the one who should first win three games of billiards should take all,
but consented to a division in proper shares when _A_ had won two games
and _B_ one, it was evident that if _A_ won the next game all would go
to him, while if he lost he would be entitled to one half. One case was
as probable as the other, therefore he was entitled to _half of these
sums taken together_; that is, to three quarters of the stakes, and _B_
to a quarter only.
99. The average speed of a motor which runs over any course at 10 miles
an hour, and returns over the same course at 15 miles an hour, is 12
miles an hour, and not 12¹⁄₂, as might be imagined. Thus a run of 60
miles out takes, under the conditions, six hours, and the return takes
four hours; so that the double journey of 120 miles is done in ten
hours, at an average speed of 12 miles an hour.
100. Farmer Hodge, who proposed to divide his sheep into two unequal
parts, so that the larger part added to the square of the smaller part
should equal the smaller part added to the square of the larger part,
had but one sheep.
Faithful to his word, he divided this sheep into two unequal parts, ²⁄₃
and ¹⁄₃, and was able to show that ²⁄₃ + ¹⁄₉ = ⁷⁄₉, and that ¹⁄₃ + ⁴⁄₉ =
⁷⁄₉. He was heard to declare further, and he was absolutely right, that
_no number larger than_ 1 can be so divided as to satisfy the conditions
which he had laid down.
The fact that _sheep_ is both singular and plural, adds much to the
perplexing points of this attractive problem.
Here is a very simple proof that the number _must be_ 1:--
Let a + b = no. of sheep
then a² + b = b² + a
a² - b² = a - b
or (a + b)(a - b) = a - b
therefore a + b = 1.
101. A horse that carries a load can draw a greater weight _up the shaft
of a mine_ than a horse that bears no burden. The load holds him more
firmly to the ground, and thus gives him greater power over the weight
he is raising from below.
102. In the six chests, of which two contained pence, two shillings, and
two pounds, there must have been at least the value of 506 pence. This
can be divided into 22 (or 19 + 3) shares of 23d. each, or 23 (19 + 4)
shares of 22d. each. Evidently then the treasure can be divided so that
19 men have equal shares, while their captain has either 3 shares or 4
shares.
103. If I bought a parcel of nuts at 49 for 2d., and divided it into two
equal parts, one of which I sold at 24, the other at 25 a penny; and if
I spent and received an integral number of pence, but bought the least
possible number of nuts, I bought 58,800 nuts, at a cost of £10, and I
gained a penny.
104. When, with a purse containing sovereigns and shillings, after
spending half of its contents, I found as many pounds left as I had
shillings at first, I started with £13, 6s.
105. When the lady replied to a question as to her age--
If first my age is multiplied by three,
And then of that two-sevenths tripled be,
The square root of two-ninths of this is four;
Now tell my age, or never see me more--
she was 28 years old.
106. If cars run, at uniform speed, from Shepherd’s Bush to the Bank, at
intervals of two minutes, and I am travelling at the same rate in the
opposite direction, I shall meet 30 in half-an-hour, for there are
already 15 on the track approaching me, and 15 are started from the
other end during my half hour’s course.
107. If it was possible to carry out my offer of a farthing for every
different group of apples which my greengrocer could select from a
basket of 100 apples, he would be entitled to the stupendous sum of
£18,031,572,350 19s. 2d.
108. If the minute-hand of a clock moves round between 3 and 4 in the
opposite direction to the hour-hand, the hands will be exactly together
when it is really 41⁷⁄₁₃ minutes past 3.
109. If the walnut monkey had stopped to help the other, and they had
eaten filberts at equal rates, they would have escaped in 2¹⁄₄ minutes.
110. The value of the cheque, for which the cashier paid by mistake
pounds for shillings, was £5, 11s. 6d. The receiver to whom £11, 5s. 6d.
was handed, spent half-a-crown, and then found that he had left £11,
3s., just twice the amount of the original cheque.
111. The number 14 can be made up by adding together five uneven figures
thus:--11 + 1 + 1 + 1. It will be seen that although only four _numbers_
are used, 11 is made up of _two figures_.
Here is another, and quite a curious solution, 1 + 1 + 1 + 1 = 4, and
with another 1 we can make up 14!
112. A business manager can fill up three vacant posts of varying value
from seven applicants in 210 different ways. For the first post there
would be a choice among 7, for the second among 6, and for the third
among 5, so that the possible variations would amount to 7 × 6 × 5 =
210.
113. If the fasting man, who began his task at noon, said it is now ⁵⁄₁₁
of the time to midnight, he spoke at 3.45 p.m., meaning that ⁵⁄₁₁ of the
remaining time till midnight had elapsed since noon.
114. If a clock takes six seconds to strike 6, it will take 12 seconds
to strike 11, for there must be ten intervals of 1¹⁄₁₅ seconds each.
115. Twenty horses can be arranged in three stalls, so that there is an
odd number in each, by placing one in the first stall, three in the
second, and sixteen (an odd number to put into any stall!) in the third.
116. The little problem, “Given _a_, _b_, _c_, to find _q_,” is solved,
without recourse to algebra, thus: _a_, _b_, _c_, = _c_, _a_, _b_; take
a cab and go over Kew Bridge, and you find a phonetic _Q_!
117. Tom Evergreen was 75 years old when he was asked his age by some
men at his club in 1875, and said--“The number of months that I have
lived are exactly half as many as the number which denotes the year in
which I was born.”
118. Eight different circles can be drawn. A circle can have one of the
three inside and two outside in three ways, or one outside and three
inside in three ways (each of the three being inside or outside in
turn), or all three may be inside, or all three may be outside, the
touching circle.
119. The way to arrange 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, so that used once
each they form a sum which is equal to 1 is this:--
35 148
-- + --- = 1.
70 296
120. The sum of the first fifty numbers may be found without any
addition thus:--The first fifty numbers form twenty-five pairs of
fifty-one each (1 + 50, 2 + 49, etc., etc.), and 51 × 25 is practically
51 × 100 ÷ 4 = 1275.
121. The tramcar _A_, which started at the same time as _B_, but ran
into a “lie by” in four minutes, and waited there five minutes till _B_
came along, when they completed their courses at the same moment in
opposite directions, could have run the whole distance in ten minutes.
122. What remains will be 8 if we take 10 and double it by writing one
10 over another so as to form 18, and then deduct 10.
123. If the average weight of the Oxford crew is increased by 2℔s., when
one of them who weighs 12 stone, is replaced by a fresh man, the weight
of that substitute is 13 stone 2℔s.
124. If a motor-car is twice as old as its tyres were when it was old as
its tyres are, and if, when these tyres are as old as the car itself is
now, their united ages will be 2¹⁄₄ years, the car is now 12 months old,
and the tyres have had 9 months’ wear.
125. _A_ and _B_, who could each carry provisions for himself for twelve
days, started to penetrate as far as possible into a desert, on the
understanding that neither of them should miss a day’s food. After an
advance of four days, each had provisions still for eight days. One gave
four portions of his store to his companion, which did not overload him,
and returned with the other four. His comrade was then able to advance
another four days’ journey, and still have rations for the eight days’
return. Thus the furthest possible penetration into the desert under the
conditions was an eight days’ march.
126. If, when a bottle of medicine and its cork cost half-a-crown, the
bottle and the medicine cost two and a penny more than the cork, the
cork cost twopence half-penny.
127. A boat’s crew far from land, with no sail or oars, and with no
assistance from wind or stream, or outside help of any kind, can regain
the shore by means of a coil of rope. Motion is given to the boat by
tying one end of the rope to the after thwart, and giving the other end
a series of violent jerks in a direction parallel to the keel. This
curious illustration of mechanical principles is from “Ball’s Mechanical
Recreations.” (_Macmillan._)
128. It will be found that after a crown and as many four-shilling
pieces as possible have been crammed into our pockets, there would still
be room for one sixpence and one threepenny-piece in some corner or
cranny. We can, therefore, have one crown, one sixpence, one
threepenny-piece, and as many four-shilling pieces as our pockets will
hold, and yet be unable to give change for a half-sovereign.
129. There were fifteen apples in the basket. Half of these and half an
apple, _i.e._, eight were first given, then half the remainder and half
an apple, _i.e._, four, then on similar lines two, leaving one in the
basket.
130. The Queer Division--
A third of twelve divide
By just a fifth of seven;
And you will soon decide
That this must give eleven--
is solved by LV ÷ V, or 55 ÷ 5 = 11.
131. A motor that goes 9 miles an hour uphill, 18 miles an hour
downhill, and 12 miles an hour on the level, will take 8 hours and 20
minutes to run 50 miles out and return at once over the same course.
132. The number of shots fired at a mark was 420 each by _A_, _B_, and
_C_. _A_ made 280 hits, _B_ 315, and _C_ 336.
133. If a dog and a cat, evenly matched in speed, run a race out and
back over a course of 75 yards in all, and the dog always takes 5 feet
at a bound, and the cat 3 feet, the cat will win, because at the turning
point the dog overleaps the half distance more than the cat does, and so
has a longer run in.
134. When a man caught up a wagon going at 3 miles an hour, which was
just visible to him in a fog at a distance of 55 yards, and which he saw
for five minutes before reaching it, he was walking at the rate of 3³⁄₈
miles an hour.
135. Three horses, _A B C_, can be placed after a race in thirteen
different ways, thus:--_A B C_, _A C B_, _B A C_, _B C A_, _C A B_, _C B
A_, or _A B C_ as a dead heat; or _A B_, _A C_, or _B C_ equal for the
first place; or _A_ first with _B C_ equal seconds; or _B_ first with _A
C_ equal seconds; or _C_ first with _A B_ equal seconds.
136. The 34 points scored against Oxbridge by the New Zealanders can be
made up in two ways, either by 8 tries and 2 converted tries, or by 3
tries and 5 converted tries.
The highest possible score on these lines is 10 tries converted,
equalling 50 points, and as the New Zealanders’ score, if all tries are
converted, becomes four-fifths of this, their actual score was 3 tries
and 5 converted into goals.
137. The smallest number, of which the alternate figures are cyphers,
which is divisible by 9 and by 11 is 909090909090909090909!
138. Our problem in which it is stated that _A_ with 8d. met _B_ and _C_
with five and three loaves, and asked how the cash should be divided
between _B_ and _C_, if all agreed to share the loaves. Now each eats
two loaves and two-thirds of a loaf, and _B_ gives seven-thirds of a
loaf to _A_, while _C_ gives him one-third of a loaf. So _B_ receives
7d. and _C_ 1d.
139. When, on opening four money-boxes containing pennies only, it was
found that those in the first with half of all the rest, those in the
second with a third of the others, those in the third with a fourth, and
those in the fourth with a fifth of all the rest, amounted in each case
to 740, the four boxes held £6. 1s. 8d., and the numbers of pennies were
20, 380, 500, and 560.
140. If two steamers, _A_ and _B_, start together for a trip to a
distant buoy and back, and _A_ steams all the time at ten knots an hour,
while _B_ goes outward at eight knots and returns at twelve knots an
hour, _B_ will regain port later than _A_, because its loss on the
outward course will not have been recovered on the run home.
141. If in London a new head to a golf club costs four times as much as
a new leather face, while at St Andrews it costs five times as much, and
if the leather face costs twice as much in London as in St Andrews, and
if, including a shilling paid for a ball, the charges in London were
twice as much as they would have been at St Andrews, the London cost of
a new head is four shillings, and of a leather face a shilling.
142. When two children were asked to give the total number of sheep and
cattle in a pasture, from the number of each sort, and one by
subtraction answered 10, while the other arrived at 11,900 by
multiplication, the true numbers were 170 sheep, 70 cattle, 240 in all.
143. If a man picks up one by one fifty-two stones, placed at such
intervals on a straight road that the second is a yard from the first,
the third 3 yards from the second, and so on with intervals increasing
each time by 2 yards, and bring them all to a basket placed at the first
stone, he has to travel about 52 miles, or, to be quite exact, 51 miles,
1292 yards.
144. When, in the House of Commons, if the Ayes had been increased by 50
from the Noes, the motion would have been carried by 5 to 3; and if the
Noes had taken 60 votes from the Ayes it would have been lost by 4 to 3,
the motion succeeded; 300 voted “Aye,” and 260 “No.”
145. There are 143 positions on the face of a watch in which the places
of the hour and minute-hands can be interchanged, and still indicate a
possible time. There would be 144 such positions but for the fact that
at twelve o’clock the hands occupy the same place.
146. If in a cricket match the scores in each successive innings are a
quarter less than in the preceding innings, and the side which goes in
first wins by 50 runs, the complete scores of the winners are 128 and
72, and of the losers 96 and 54.
147. When a ball is thrown vertically upwards, and caught five seconds
later, it has risen 100 feet. It takes the same time to rise as to fall,
and when a body falls from rest, it travels a number of feet represented
by sixteen times the square of the time in seconds.
Hence comes the rule that the height in feet of a vertical throw is
found by squaring the time in seconds of its flight, and multiplying by
four.
148. The carpet which, had it been 5 feet broader and 4 feet longer,
would have contained 116 more feet, and if 4 feet broader and 5 longer
113 more, was 12 feet long and 9 feet broad.
149. When, in estimating the cost of a hundred similar articles,
shillings were read as pounds, and pence as shillings, and the estimated
cost was in consequence £212, 18s. 4d. in excess of the real cost, the
true cost of each article was 2s. 5d.
150. If the square of the number of my house is equal to the difference
of the squares of the numbers of my next door neighbours’ houses, and if
my brother in the next street can say the same of his house, though its
number is not the same as that of mine, our houses are numbered 8 and 4.
In my street the even numbers are all on one side, in my brother’s
street they, run odd and even consecutively, and so 8² = 10² - 6², and
4² = 5² - 3².
151. When two men of unequal strength have to move a block which weighs
270 ℔s., on a light plank 6 feet long, if the stronger man can carry 180
℔s., the block must be placed 2 feet from him, so that he may have that
share of the load.
152. If a man who had twenty coins, some shillings, and the rest
half-crowns, were to change the half-crowns for sixpences, and the
shillings for pence, and then found that he had 156 coins, he must have
had eight shillings at first.
153. If, when coins are placed on a table at equal distances apart, so
as to form sides of an equilateral triangle, and when as many are taken
from the middle of each side as equal the square root of the number on
that side, and placed on the opposite corner, the number on each side is
then to the original number as five is to four, there are forty-five
coins in all.
154. When the gardener found that he would have 150 too few if he set
his posts a foot apart, and seventy to spare if he set them at every
yard, he had 180 posts.
155. In order to buy with £100 a hundred animals, cows at £5, sheep at
£1, and geese at 1s. each, the purchaser must secure nineteen cows, one
sheep, and eighty geese.
156. If John, who is 21, is twice as old as Mary was when he was as old
as Mary is, Mary’s age now is 15³⁄₄ years.
157. If in a cricket match _A_ makes 35 runs, and _C_ and _D_ make
respectively half and a third of _B_’s score, and if _B_ scores as many
less than _A_ as _C_ scores more than _D_, _B_ made 30, _C_ 15, and _D_
10 runs.
158. The least number which, divided by 2, 3, 4, 5, 6, 7, 8, 9, or 10,
leaves remainders 1, 2, 3, 4, 5, 6, 7, 8, 9, is 2519, their least common
multiple less 1.
159. A square table standing on four legs, which are set at the middle
points of its sides, can at most uphold its own weight upon one of its
corners.
160. The division of ninety-nine pennies, so that share 1 exceeds share
2 by 3, is less than share 3 by 10, exceeds share 4 by 9, and is less
than share 5 by 16, is 17, 14, 27, 8, and 33.
161. If Indians carried off a third of a flock and a third of a sheep,
and others took a fourth of the remainder and a fourth of a sheep, and
others a fifth of the rest and three-fifths of a sheep, and there were
then 409 left, the full flock was 1025 sheep.
162. When a cistern which held fifty-three gallons was filled by three
boys, _A_ bringing a pint every three minutes, _B_ a quart every five
minutes, and _C_ a gallon every seven minutes, it took 230 minutes to
fill it, and _B_ poured in the final quart, _A_ and _C_ _coming up one
minute too late_ to contribute at the last.
163. A man who said, late in the last century, that his age then was the
square root of the year in which he was born, was speaking in the year
1892.
164. If when a dealer in curios sold a vase for £119, his profit per
cent., and the cost price of the vase, were expressed by the same
number, it had cost him £70.
165. The chance of throwing at least one ace in a single throw with a
pair of dice is ¹¹⁄₃₆, for there are five ways in which each dice can be
thrown so as not to give an ace, so that twenty-five possible throws
exclude aces. Hence the chance of _not_ throwing an ace is ²⁵⁄₃₆, which
leaves ¹¹⁄₃₆ in favour of it.
166. The policeman who ran after a thief starting four minutes later,
and running one-third faster, if they both ran straight along the road,
caught him in twelve minutes.
167. At a bazaar stall, where twenty-seven articles are exposed for
sale, a purchaser may buy one thing or more, and the number of choices
open to him is one less than the continued product of twenty-seven twos,
or 134217727.
VERY PERSONAL
168. When Nellie’s father said:--
I was twice as old as you are
The day that you were born.
You will be just what I was then
When fourteen years are gone--
he was 42, and she was 14.
WORD AND LETTER PUZZLES
1. The word square is completed thus:--
MEAD
EDGE
AGUE
DEED
2. The word square filled in is:--
CIRCLE
INURES
RUDEST
CREASE
LESSEE
ESTEEM
_Notice the curious diagonal of E’s._
3. In the incomplete sentence,
SO****AG****LATI****X****ITH
the duplicate letters are filled in thus:--
SOME MEAGRE RELATIVE VEXED EDITH
The two last letters of each word are repeated as the two first of the
word that follows.
4. The word square is completed thus:--
WASTE
ACTOR
STONE
TONIC
ERECT
5. By twice building up two Ds into a B we make BULBOUS.
6. The question put on paper to the love-lorn youth, “Loruve?” is, when
interpreted, “Are you in love?” and the advice given to him on another
slip, “Prove
L
A F
D
and ensure success,” reads into, “Prove a fond lover, and ensure
success” (a f _on_ d l _over_).
7. DOUBLE ACROSTIC ST. JAMES’ GAZETTE
S . . . prin . . . G
T . . . ar . . . A
J . . . abe . . . Z
A . . . t . . . E
M . . . omen . . . T
E . . . mme . . . T
S . . . trik . . . E
8. The completed word square is--
AMENDS
MINION
ENABLE
NIBBLE
DOLLAR
SNEERS
9. The oracular response to a young Frenchman at a _fête_, who inquired
how he could best please the ladies--
MEC DO BIC
conceals this sage advice--
Aimez, cédez, obéissez!
Love, yield, obey!
10. The solution to our Letter Fraction Problem is of a verbal
character. The original statement
15844
m
--
ot = mo
--
y
is dealt with thus:--
m _on_ ot _on_ y = mo _not on_ y, and so the word monotony solves the
equation.
11. The buried beasts are _chamois_, _buffalo_, _heifer_, and _leopard_;
and when the Oxford athlete cries--
“Though I jump and row and run,
Cap or cup I never won”
he introduces us to a _porcupine_.
12. The lines--
Fourteen letters here we fix,
Vowels only two are spoken;
All together these we mix
Into what can not be broken--
is solved by _indivisibility_, which has many an _i_, like a peacock’s
tail.
13. The English word of thirteen letters in which the same vowel occurs
four times, the same consonant six times, another twice, and another
once, is _Senselessness_.
14. The condensed proverb “WE IS DO” reads at its full length as “Well
begun is half done.”
15. This is the completed word square:--
WASHES
ARTERY
STORMS
HERMIT
ERMINE
SYSTEM
16. Dr Whewell’s puzzle lines--
O O N O O.
----------
U O A O O I O U,
O N O O O O M E T O O.
U O A O I D O S O
I O N O O I O U T O O!
read thus:--
OH SIGH FOR NO CIPHER
You sigh for a cipher, O, I sigh for you,
Sigh for no cipher, O sigh for me too.
You sigh for a cipher, I decipher so,
I sigh for no cipher, I sigh for you too!
17. This is the completed diamond:--
P
POR
CORES
FORCEPS
PORCELAIN
REFLECT
SPACE
SIT
N
18. The medley--
Tan HE Edsa VEN in
It N Gja SmeTs AsgN
aD Az Rett De
is read by taking first the capitals in their order, and then the small
type. It comes put out as “The Evening Standard and Saint James’s
Gazette.”
19. The statement, I can travel first-class on the G.E.R. from
2222222244444500, reads into--from 22 to 2 to 22 to 4 for 44 4d; or, in
plain terms, from 1.38 to 3.38 for 14s. 8d. This works out at about 3d.
a mile, the usual allowance for first-class, for two hours, at about 29
miles an hour.
20. A CURIOUS OLD INSCRIPTION
Read the inscription backwards, and it resolves itself into the lines
familiar to us in our childhood:--
Ride a cock horse to Banbury Cross
To see a fine lady ride on a grey horse.
Rings on her fingers and bells on her toes,
She shall have music wherever she goes!
21. The reason why the invitation to Jack to sample the Irish stew at
Simpson’s was to be kept in mind by the catch words--
Join me at and
i
s,
is because if you join _me_ and _at_, and note that _and_ is _on i_,
which is _on s_, you arrive at the suggestive sentence--_meat and
onions_.
22. The labourer’s quaint letter, which ran “Cepatomtogoatatrin,” was,
in plainer English, “Kept at home to go a tatering.”
23. Our double acrostic comes out thus:--
PROBLEM--PUZZLES
P ........a....... P
(T) R ................ U (E)
O ................ Z
B ........o....... Z
L .......eve...... L
E ........v....... E
M ................ S
24. The Hidden Proverb is--
“Necessity is the mother of invention.”
25. The “deed done” in our Will puzzle is the making in Roman numerals
of “Codicil.” The lawyer was to set down, a hundred, to add nothing, to
set down five hundred, then one, then another hundred, and then one
more, and, finally, fifty, and accordingly he wrote upon the parchment
the one word CODICIL.
26. The word square is--
EDITOR
DESIRE
ISLAND
TIARAS
ORNATE
REDSEA
27. The notes of music A. G. A. E. A. over the grave of a French
musician, who was choked by a fish bone, are in the French notation, “La
sol la mi la,” which reads into “La sole l’a mis 1à.”
Similarly the inscription over the porch of Gustave Doré’s house C. E.
B. A. C. D. is equivalent to “Do, mi, si, la, do, re,” which may be
taken to represent “Domicile à Doré.”
28. When his best girl said to Jack Spooner, “We can go to-morrow at
222222222222 LEY STREET,” he understood her to mean, “We can go
to-morrow, at two minutes to two, to two twenty-two, to 222 Tooley
Street.”
29
C
---------- spells _contents_ (c on ten ts!).
TTTTTTTTTT
30. We can treat the word _disused_ so as to affirm or to disallow the
use of its initial or final d, for we can write it _d is used_, or
_disuse d_!
31. The title of the book shaken up into
EIOOOU
BCNNRRSS
is “Robinson Crusoe.”
32. If the letter M only is inserted in the proper places in the line--
A DEN I I CAN DOCK
it will read: _Madmen mimic and mock_.
33. The quotation from Shakespeare--
OXXU8 MAAULGIHCTE
NOR
is by interpretation:--“Nothing extenuate, nor set down aught in
malice.”
34. The phonetic nightmare--
Ieukngheaurrhphthewempeighghteaps--
is merely the word _unfortunates_. It can be justified thus by English
spelling of similar sound taken letter by letter:--
u--iew in view; n--kn in know; f--gh in tough; o--eau in beau; r--rrh in
myrrh; t--phth in phthisis; u--ewe; n--mp in comptroller; a--eigh in
neigh; t--ght in light; e--ea in tea; and s--ps in psalm.
35. The word square is completed thus:--
FARM
AREA
RENT
MATE
36. A QUAINT INSCRIPTION
The millers leave the mill,
The wherrymen lower their sail;
The maltsters leave the kiln,
For a drop of the White Swan’s ale.
37. A POET’S PI
TONDEBNIOTOCHUMFOARYHUR
OTDIRECTTHAWHOTERSOFKLSYA;
TIKATESTUBALIGHTSTILLETRUFLYR
OTBOWLALLNFESLEAVARFWYAA
is disentangled thus:--
Don’t be in too much of a hurry
To credit what other folks say;
It takes but a slight little flurry
To blow fallen leaves far away.
38. BURIED PLACES
The five buried places are Deal, London, Esk, Perth, and Baden. The word
is Ourangoutang.
39. It is no offence to conspire in the evening, because what is
treasonable is _reasonable after t_!
40. The bit of botany--
Inscribe an _m_ above a line,
And write an _e_ below,
This woodland flower is hung so fine
It bends when zephyrs blow--
is solved by,
m
-,
e
_an em on e_, the delicately hung wind-flower.
41. A PIED PROVERB
The pied proverb, is “A rolling stone gathers no moss.”
42. The Drop Letter Proverb--
E..t. .e.s..s .a.e .h. .o.. ..i.e, is--_Empty vessels make the most
noise_.
43. The English word of five syllables, which has eight letters, five of
them vowels--namely an a, an e, twice i, and y--is _Ideality_.
44. TORMENT may be turned into RAPTURE, using four links, changing only
one letter each time, and varying the order of the letters, thus:
TORMENT, _portent_, _protest_, _pratest_, _praters_, RAPTURE.
45. The pied sentence--
a a c e e e f f h h i i i i i m n n o o o p r r s s t t t t t
can be cast into the proverb--
“Procrastination is the thief of time.”
46. The English sentence, when the letter _o_ is added, reads:--
“Good old port for orthodox Oxford dons.”
47
One vowel in an English word is found,
Which by eight consonants is hedged around--
is solved by _Strengths_.
48. The letters AAAAABBNNIIRSSTT form the word _Antisabbatarians_.
49. The quotation from Shakespeare,
KINI
stands for “A little more than kin, and less than kind.”
50. The two English words which have the first six letters of the
alphabet among their ten letters are _fabricated_ and _bifurcated_.
51. SHIFTING NUMBERS
The letter _A_ stands at the head of the letters of the alphabet. For
_bed_ 3 of these are used; for _goal_, 4; for _prison_, 6; for _six_, 3;
for _three_, 5. The letter _A_ is not used in the spelling of the name
of any number from 1 to 100, but it makes up, with the other vowels, the
number 6.
52. The prodigal’s letter to his father, “Dear Dad, keep 1000050,” in
reply to a suggestion for safeguarding some of his prospects, was
written in playful impudence; and its interpretation is, “Dear Dad, keep
cool!” for the figures in Roman numerals are COOL.
53. BURIED POETS
The poets’ names buried in the lines--
The sun is darting rays of gold
Upon the moor, enchanting spot;
Whose purpled heights, by Ronald loved,
Up open to his Shepherd cot.
And sundry denizens of air
Are flying, aye, each to his nest;
And eager make at such an hour
All haste to reach the mansions blest.
are Gray, Moore, Byron, Pope, Dryden, Gay, Keats, and Hemans.
54. When _A. B._ gave up the reins of government, and _C.B._ took office
in his place, the two verbs, similar in all respects, except that the
one is longer by one letter than the other, which expressed the change,
were _resigns_--_reigns_.
55
Underdone mutton and onion make between you and me,
A glutton a little seedy after a capital tea.
56
First a _c_ and _a t_, last _a c_ and a _t_,
With a couple of letters between,
Form a sight that our eyes are delighted to see,
Unless in their sight it is seen--
is solved by _Cataract_. The first line reads, First a _c_ and _a t_,
last _a c_ and a _t_, that is _cat_ and _act_.
57. Cuba.
58. The Rebus T S is solved by the words _tones_ and _tans_, _t_ before
_one s_, or _t_ before _an s_.
59. The phonetic phrase--
INXINXIN--
is, _Ink sinks in_!
A GOOD END
60. Finis (F IN IS).
=PART III.=
CONTENTS
PAGE
WORD PUZZLES, MISSING WORDS, LETTER PUZZLES III-1
ANAGRAMS, PICTURE PUZZLES III-48
PALINDROMES III-108
SOLUTIONS III-111
WORD PUZZLES
No. I--AN EARLY CRYPTOGRAM
The use of some sort of grille was not uncommon in olden days among the
many methods then employed for secret correspondence. Here is an early
and interesting specimen:--
[Illustration: VENITE PAUPERES]
An important despatch would appear to be a mere confusion of letters,
until it fell into the right hands, and this perforated key was laid
over it, when the intended instructions were at once revealed, and read
in the openings of the tracery.
No. II.--A MANIFOLD MONOGRAM
Here, by seven straight lines and one circle, a manifold monogram is
formed.
[Illustration]
Within its borders we find a circle, a square, a parallelogram, a
triangle, the vowels a, e, i, o, u; the consonants, C, D, H, K, L, M, T,
W; and other forms and figures.
MISSING WORDS
1. PICKING AND STEALING
What tempting ...... beguiled the boy to sample
Fruit that hung ...... on the parson’s trees?
...... upon ...... shall make him an example
When the stern ...... has brought him to his knees.
The missing words are spelt with the same six letters.
No. III.--A BOOK AND ITS AUTHOR
What well-known book and its author may be represented thus:--
[Illustration]
2. A SWARM OF MISSING WORDS
No less than eight different words, spelt with the same six letters, are
available to fill the gaps in the following lines:--
Man of the dark room, ...... none I find
Upon these ...... of likeness to my features.
...... then nought, O man of evil mind,
Who ...... thus to libel fellow-creatures?
Evil thus done ...... upon the doer,
The ...... in thy conduct, Sir, are many;
...... thy life, and let thy crimes be fewer,
Or all thy ...... of good won’t fetch a penny!
No. IV.--ON THE SHUTTERS
Upon the shutters of a barber’s shop the following legend was painted in
bold letters:--
NO. I
JOHN MARSHALL
IN ATTENDANCE
FROM 8 A.M. DAILY
BARBER AND
HAIR CUTTER
THE BALD CRY ALOUD
FOR HIS CREAMS
AS DISPLAYED IN THIS WINDOW
WHICH MAKE HAIR GLISTEN
CLOSES AFTER 8 P.M.
One evening about 8.30, when it was blowing great guns, quite a crowd
gathered round the window, and seemed to be enjoying some excellent
joke. What was amusing them when one shutter blew open?
3. NO HEART!
False Kate! ... .... . ......’s nest,
.. ..... the Upas tree,
I will not budge, ... .... to rest,
.. .... . coward be.
No, not .... ... enough their sting
To drive me back to thee;
None swifter meet thy beckoning
.... ... the hills I flee.
... .... frosts less my love would quell.
Rather than seek thy side,
Of ... .... horse I love so well
I’ll ... .... hoofs and hide!
The number of letters in each word of the missing phrases is indicated
by dots, and the seven letters in each case are those that spell also
“no heart,” which we give as a title and clue.
No. V.--A PHONETIC MAXIMUM
How far phonetic spelling may be pushed, is illustrated by the following
swarm of variations given in a book published at Enfield in 1829:--
Scissars -- ers -- irs -- ors -- urs -- yrs
Scisars -- „ -- „ -- „ -- „ -- „
Sciszars -- „ -- „ -- „ -- „ -- „
Scizars -- „ -- „ -- „ -- „ -- „
Scizscars -- „ -- „ -- „ -- „ -- „
Scizzars -- „ -- „ -- „ -- „ -- „
Or the word may start with Sis, Siss, Siz, Sys, Syss, Syzz, Syzs, Syz,
Cis, Ciss, Ciz, Cisz, Cysz, Cyz, Cyzz. By substituting “z” for the final
“s” we may double the number, and reach a total of 1224.
4. UNNATURAL HISTORY
’Neath ...... Indian seas fierce battles spread
’Twixt ...... hermit-crabs and other shellfish!
With horrid ...... when their foes are dead,
These crabs declare their shells ......, so selfish!
Each missing word has the same six letters.
No. VI.--SOLVITUR AMBULANDO
On this chequered floor, paved with slabs each a foot square, the
palindrome word ROTATOR can be traced in various ways.
+---+---+---+---+---+---+---+---+---+---+---+---+---+
|=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=|
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| O |=R=| O | T | A | T | O | T | A | T | O |=R=| O |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| T | O |=R=| O | T | A | T | A | T | O |=R=| O | T |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| A | T | O |=R=| O | T | A | T | O |=R=| O | T | A |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| T | A | T | O |=R=| O | T | O |=R=| O | T | A | T |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| O | T | A | T | O |=R=| O |=R=| O | T | A | T | O |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
|=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=|
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| O | T | A | T | O |=R=| O |=R=| O | T | A | T | O |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| T | A | T | O |=R=| O | T | O |=R=| O | T | A | T |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| A | T | O |=R=| O | T | A | T | O |=R=| O | T | A |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| T | O |=R=| O | T | A | T | A | T | O |=R=| O | T |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| O |=R=| O | T | A | T | O | T | A | T | O |=R=| O |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
|=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=|
+---+---+---+---+---+---+---+---+---+---+---+---+---+
If a man walks over it, taking one slab at every step, and never
lengthening his strides, how many steps will he take in tracing every
possible variation of the word, and how many such variations are there?
No. VII.--A CURIOUS CHRONOGRAPH
A bachelor clergyman, whose initials were I.E.V., had built a fernery
with the profits of his tracts on the deceased wife’s sister question.
He dated it on a mural tablet thus:--
| |
-+------------------------------------+-
|My LateVVIfe’ssIsterbVILtthIs VVaLL;|
| bVt I In trVth |
| neVer VVeD any VVIfe at aLL, |
| nor VVont forsooth, |
| saIth I. e. V. |
-+------------------------------------+-
| |
If the Roman numerals are extracted from this inscription, and added
together, they amount to 1884, the desired date.
5
Though ------ secure and ------ in his cage,
Our Polly, when ------, will fly into a rage.
Each missing word has the same six letters.
6
All courtly honours are but light
As grains that from a ------ fly;
And he who wears the ------ bright
May haply in a ------ die.
The missing words are spelt with the same six letters.
7
I’d rather from a ------ eat,
I give my sacred word,
Than dine in slums where ------ meet,
And ------ pedlars herd.
Each missing word has the same six letters.
No. VIII.--AN OLD SAMPLER
In the drawer of a cabinet that had belonged to my grandmother I came
upon an old sampler, beautifully worked in scarlet cross-stitch. Its
very curious legend runs as follows:--
| |
-+-----------------------------+-
| AL. IT. |
|T.L EW. O. MA! |
|N.T. Ho! UGH. AVE. Ryli. |
|T.T. Let. Hi! N.G.I. |
|S.S. We. Et. Erf. Art. Ha!|
|N.S. Ug. Ara. N.D.F. Lo! |
|W.E. R.S.T. Ha! TB. |
|L.O. O! Mins. Pri. |
| N. G. |
-+-----------------------------+-
| |
8
A much married ....... of Cadiz
Once ....... some riotous ladies.
To ....... him they chucked
A ......., but he ducked,
Which ....... these rude ladies of Cadiz.
The five missing words are spelt with the same seven letters.
9. THE LASS AND HER LOVER
A lass and her lover were ------ by the sky
Not to ------ too far where no shelter was nigh.
She lingered behind, and ----- -- old church,
St. ------ by name, and was left in the lurch.
She tried a short cut through a park on the grass,
But sternly the ------- forbade her to pass;
Then helplessly stood the disconsolate maid,
When the lad she was soon to --- --- to her aid.
The missing words are spelt with the same six letters.
No. IX.--THE LANDLORD’S PUZZLE
The following curious Missing Words Puzzle is to be seen on a card which
hangs in the bar of an inn in the Isle of Man:--
I had both-- |by both I set great store |and a--
I lent my-- |and took his word therefor;|to my--
I asked my-- |and nought but words I got.|from my--
I lost my-- |for sue him I would not. |and my--
At length with--|which pleased me very well,|came my--
I had my-- |away quite from me fell: |but my--
If I’d both-- |as I have had before, |and a--
I’d keep my-- |and play the fool no more. |and my--
It is to be read thus:--
I had both _money_ and a _friend_, by both I set great store,
I lent my _money_ to my _friend_, and took his word therefor,
_and so on to the end_.
10
When ------- smiles, and sunbeams play
On flowers that ------- and deck the green,
------- can match the scene so gay
------ they crown the May-day queen?
The missing words are spelt with the same seven letters.
11
’Tis said of William, while his forces rested
On Albion’s ------, when Harold had been bested,
He made the ------ of his ------ fuse
Saxon spear-heads, to fashion into shoes.
Each missing word has the same six letters.
No. X.--DECAPITATED WORDS
The decapitated words are in italics:--
The ship rode in an _eastern_ bay,
Asleep _astern_ the master lay,
A _stern_ and rugged man was he,
And, like a _tern_, at home at sea.
Like swooping _ern_ he caught his prey
Whene’er an _R.N._ came his way;
But while due _N._ the needle kept
He in his cabin lay and slept.
The ern, or erne, is the sea-eagle.
12
Happiness, brighter than ------, is dead;
Life’s battle, sterner and ------ now,
Heals the sore ------ that love left as it fled,
------ remembrance of long broken vow!
The missing words are spelt with the same six letters.
13. AN AUTHOR’S EPIGRAM
Press critics fall on me like sharks;
“A shameless ....... of odds and ends,
No ....... original,” and more remarks
In adverse mood. But stay, my friends,
He ....... best who hath his record clean;
My faults are published, yours are yet unseen!
The missing words have the same seven letters.
14
...... are his ......, fashion-forms of grace
In ...... deftly hinted.
...... soft as ......, crowned by Beauty’s face,
In ...... hues are tinted.
The six missing words are spelt with the same six letters.
No. XI.--AN ANCIENT ANAGRAM
On the front of a church, in the Largo Remedios, at Braga, in Portugal,
there is an inscription which, with its letter-perfect Anagram, runs as
follows:--
| |
-+----------------------------+-
| BEATUS IOANNES MARCUS |
| CHRISTI DOMINI DISCIPULUS |
| ---- |
| ANAGRAM |
| -------------- |
|IS IN MUNDO PIUS EST MEDICUS|
| TUIS INCOLIS, BRACHARA |
| -----*----- |
-+----------------------------+-
| |
which may be rendered--“Blessed John Mark, disciple of Christ the Lord.”
_He in this world is the holy healer of thy people Braga!_
15
When Kate --- -------- ----- -------- displayed
----- ----- --- hide a tear;
“All love is dead --- --------,” he said.
“------- I’ll ----- --------!”
The missing word and groups of words are spelt with the same seven
letters.
16
Some grinding at the ------ must toil,
Down-trodden ------ of to-day;
While other children of the soil
In vast ------ their wealth display.
The missing words are spelt with the same six letters.
No. XII.--STRIKE A BALANCE
This diagram shows that the odd numbers of the 9 digits add up to 25,
and the even numbers to 20.
+----------------------+
/| |\
+-+----------------------+-+
| | 1 | |
| | 3 2 | |
| | 5 4 | |
| | 7 6 | |
| | 9 8 | |
| | -- -- | |
| | 25 20 | |
| | ======== | |
+-+----------------------+-+
\| |/
+----------------------+
Can you arrange the 9 digits in two groups in which the odd numbers and
the even will add up to exactly the same sum?
17
Betrayed by faithless friends, in ------ mood
Man ------ his fellows as the ------ brood.
The missing words are spelt with the same six letters.
18. HONEST INDIAN
With divers ---- his ---- is scarred,
He hangs a bangle in his nose;
Such marks secure his ---- regard,
Exalt his fame, and ---- his foes.
Each missing word is spelt with the same four letters.
No. XIII.--HKISTA!
MRS LR’S SR
MR LR KRS.
“BLR MR LR!”
MRS LR HRS.
How do you read these lines and their title?
19. ON THE OCEAN WAVE
------- who, as we ------- roll,
------- for me the foaming bowl,
And ------- off unfriendly spray
With oilskin cape, thou shalt not say
“In vain I’ve ------- my favours here.”
I’ll think of thee when port is near!
The four missing words are spelt with the same seven letters.
20. THE ZENANA MISSION
With high ------ for hearts and hands,
These ------ ------ for distant lands.
The three missing words are spelt with the same six letters.
21
The ------- of his speech did not
------- his audience a jot.
They greeted all he said thereafter
With -------, smiles, and open laughter.
The missing words have the same seven letters.
22
To convent shrine at break of day
With ----- together nuns repair;
Mid gleaming ----- they kneel and pray,
And chanted ----- allays each care.
Spelt with the same five letters.
No. XIV.--IN MEMORIAM
The following puzzle-epitaph was engraved on a tombstone in Durham
Cathedral:--
| |
-+-------------------------+-
|WEON . CEW . ERET . WO|
|WET . WOM . ADEO . NE|
|NON . EFIN . DUST . WO|
|NO . WLI . FEB . EGO . NE|
| WILLIAM and MARGARET |
| TAYLOR |
| Anno Domini 1665. |
-+-------------------------+-
| |
23
Here once, as a hag is bedizened with paint,
A ----- ----- ----’- in the garb of a saint.
The three missing words are spelt with the same five letters.
24. IN PRAISE OF SUSSEX
Sussex! No ----- of a bygone age
Ride through thy ----- to-day with shield and -----,
And ----- no horseflesh so they may engage
To save some damozel from harm or fear.
Who now would give a thought to ----- or peaches?
He truly farms who ----- a golden store;
And, though he cannot ----- the simplest speeches,
----- down expense, and savings has galore!
Each missing word is spelt with the same five letters.
No. XV.--A FRENCH WORD SQUARE
Here is an excellent French Word Square of seven letters:--
+-+-+-+-+-+-+-+
|R|E|N|E|G|A|T|
+-+-+-+-+-+-+-+
|E|T|A|L|A|G|E|
+-+-+-+-+-+-+-+
|N|A|V|I|R|E|S|
+-+-+-+-+-+-+-+
|E|L|I|D|A|N|T|
+-+-+-+-+-+-+-+
|G|A|R|A|N|C|E|
+-+-+-+-+-+-+-+
|A|G|E|N|C|E|R|
+-+-+-+-+-+-+-+
|T|E|S|T|E|R|A|
+-+-+-+-+-+-+-+
This is a worthy companion to the English seven-letter squares on
“Problem” and “Palated,” which are given on other pages.
25
----- in the ----- far away,
Remote alike from heaven and hell,
The silent -----, so poets say,
Who shape the ends of mortals dwell.
Each missing word has the same five letters.
26
In all our ------ the mechanician’s skill
Now compasses the rogue with artful wile.
The patent ------ and the “tell tale” till
Beset his way who ------ the path of guile,
Besotted youth, who ------ to defy
The rule of right, beware his awful fate
Who, sitting down to eat a stolen pie,
------ the eighth commandment on the plate!
Spelt with the same six letters.
No. XVI.--A QUAINT EPITAPH
This epitaph, most of it in some sort of dog Latin, tells its own
pathetic tale on its tablet.
| |
-+------------------------------+-
|IT - OBIT - MORTI - MERA |
|PUBLI - CANO - FACTO - NAM |
|AT - RES - T - M - ANNO - XXX |
|ALETHA - TE - VERITAS |
|TE - DE - QUA - LV - VASTO |
|MI - NE - A - JOVI - ALTO |
|PERAGO - O - DO - NE - AT |
|STO - UT - IN - A - POTOR - AC|
|AN - IV - VAS - NE - VER - A |
| =R - I - P= |
-+------------------------------+-
| |
27
The .... with .... importunate
To rule his .... may try;
His .... is so unfortunate
That .... they may reply!
The missing words are spelt with the same four letters.
28. “TURN AGAIN WHITTINGTON!”
In all the pomp of ---- and chains
He lords it o’er the town;
The ---- of his hopes he gains
Who ---- with half-a-crown.
Each missing word has the same four letters.
No. XVII.--A TRAGIC CALENDAR
| |
-+--------------------------------------+-
|Jan-et was quite ill one day; |
|Feb-rile troubles came her way. |
|Mar-tyr like, she lay in bed, |
|Apr-oned nurses softly sped. |
|May-be, said the leech judicial, |
|Jun-ket would be beneficial. |
|Jul-eps, too, though freely tried, |
|Aug-ured ill, for Janet died. |
|Sep-ulchre was sadly made, |
|Oct-aves pealed and prayers were said.|
|Nov-ices with many a tear |
|Dec-orated Janet’s bier. |
-+--------------------------------------+-
| |
29. A SAUCY JADE
A writer quite devoid of tact,
She valued ------ more than fact.
A wayward ------ she made her muse
On ------ and noble heaped abuse.
Dealt ----- on ------ to prince or peer,
Her ----- wit a paltry jeer.
Each missing word is spelt with the same six letters.
30. MISSING WORDS
Of all destructive country pests
The farmer ..... ..... least;
He cannot yet the puzzle .....
How to suppress the beast!
The missing words have the same five letters.
No. XVIII.--A DIAMOND PALINDROME
Within the four corners of this Mystic Diamond the Palindrome, NAME NO
ONE MAN, can be traced in 16,376 different directions, in straight
lines, or at right angles, starting from the centre or from the borders.
N
NaN
NamaN
NamemaN
NamenemaN
NamenonemaN
NamenooonemaN
NamenoonoonemaN
NamenoonenoonemaN
NamenoonemenoonemaN
NamenoonemamenoonemaN
NamenoonemaNamenoonemaN
NamenoonemamenoonemaN
NamenoonemenoonemaN
NamenoonenoonemaN
NamenoonoonemaN
NamenooonemaN
NamenonemaN
NamenemaN
NamemaN
NamaN
NaN
N
31. TO THE FRESH AIR FUND
OH THE ------ OF THE ------.
The ------ of darkest London are radiant with ------,
You can ----- it in their ----- little faces.
So wherever you ------ let it be your heart’s ------
To ease the ----- and sorrows of all -----.
The missing words in the title and those in the first and third lines
each contain six letters. Those in the second four, and in the fourth
five.
No. XIX.--SHAKESPEARE RECAST
If you start with the right letter in this combination, and then take
every third letter, a well-known quotation from Shakespeare will be
formed.
+----------------------+
|HOUSE.CANOE.AFTER. |
|HOUR.PRINT.CAVE.CHILD |
|SASH.SLEVE.ACORN. |
|AMPLE.SAD.TATTA.HENA |
|MAT.ACHE.CAKE.TACHES. |
|HELIAC.SACQUE.USUAL. |
|ARBOR.SEE.MULCH.JACUR.|
|USE.STOP. |
+----------------------+
32. THE FLIRT THAT FAILED
She ...... in vain, “Men are ......, and as shy
As ...... in October,” she says with a sigh.
The missing words are spelt with the same six letters.
33
When good men lapse the ....... grins,
When one ....... he swears,
And strives to set his former sins
Against his ....... prayers.
Each missing word is spelt with the same seven letters.
No. XX.--A DOUBLE ACROSTIC
An old Italian bird we know
Whose heart is ever touched by snow.
1. None can press me without pain
Pressure is against the grain.
2. I am a king without my head.
3. Here is another king instead.
It is fair to our readers to say that some knowledge of Latin and French
is needed for dealing with this very excellent Acrostic, of which a full
explanation is given with the solution.
34. THE GIPSY LAD
His hands and face were -----, and sad
Upon the ----- a gipsy lad
Lay; as the breeze his temples fanned
He counted ----- on either hand.
Each missing word has the same five letters.
35. THE OLD DIVINE
In yon grey ----- an old divine
Taught me my ----- to decline,
And verbs with ----- of mood and tense;
But while I plodded on apace
I had to keep the ----- of grace,
And close his prayers with loud -----.
Each missing word is spelt with the same five letters.
36. BANZAI!
No reckless ------ of the sword,
He ------ his fatherland to save.
Fighting for freedom, not ------,
Now ------ of the eastern seas.
The four missing words contain six letters.
No. XXI.--HIDDEN PROVERBS
Five familiar proverbs are hidden in this square of 169 letters.
R E N O W N E D T H A N W
S Y O U R C A K E A N D A
S T E T O B E F E A R H R
E A R K S S P O I L E A F
L E O O H E R S N T D V O
O T M O T L I N O H T E U
N O S C A L A G M E H I R
S N I Y G O R S O B A T S
E N G N E N O T S R N P A
I A O A M O O T S O A E W
R C D E V I L A H T D A S
O U O Y N O I L D A E C A
T C I V R E H H T A H E Z
The proverbs are arranged in a regular sequence.
37. OF DOUBTFUL WORTH
A fair ------, though ------ and frayed,
The critic ------ to own,
And it might interest the trade
If ------ by some one known.
The missing words are spelt with the same six letters.
38
In his ------ days, as when he was young,
The ------ indulges in ------ of tongue.
Each missing word is spelt with the same six letters.
No. XXII.--AN ALPHABETICAL TOAST
Lord Duff, who evidently had a turn for puzzles, proposed this
alphabetical toast, which became popular among the Jacobites.
A.B.C. A blessed change.
D.E.F. Down every foreigner.
G.H.J. God help James.
K.L.M. Keep Lord Mar.
N.O.P. Noble Ormond preserve.
Q.R.S. Quickly resolve Stuart.
T.U.V.W. Truss up vile Whigs.
X.Y.Z. Exert your zeal.
Another quaint and ingenious use of separate letters is recorded of the
well-known preacher, Henry Ward Beecher.
Years ago, before his reputation had become world-wide, he was asked to
give a lecture without charge, and assured that it would increase his
fame. His reply was characteristic and very much to the point: “I will
lecture for F.A.M.E.--fifty and my expenses!”
39. MISSING WORDS
(1) A cylindrical lock
Where no key can be found,
(2) An instrument treble
And ringing in sound.
(3) In story-land ranging,
(4) Now chopping and changing;
(5) Broken up, reunited,
Quite whole I am found.
Words, spelt with the same eight letters are indicated in these lines.
There are two words in (1).
No. XXIII.--A MORAL PRECEPT
The following obscure legend was worked on an old sampler, in the red
cross-stitch that found favour when our grandmothers were girls:--
+----------------+
| Elizabeth out |
|Rue Constantine |
|Very thin gloves|
| Way Susan dart.|
+----------------+
This was evidently some excellent moral precept, but it hung on its
frame, a mere puzzle on the school-room wall, until an expert word
juggler came that way, and solved the mystery by reading it off thus:--
“Eliza be thou true, constant in everything. Love sways us, and art.”
40
In the following lines the first missing word has two letters, and the
letters are carried on, with one more added each time, and in varied
order, throughout the verses, either in single words or in groups of
words:--
A lover of .. unkind fair
Were less than ... did he not ....
“Mine is no ..... life, I swear,
It dwells in this ...... alone.
Grant me thy love, like ....... chaste
.. ...... lest thou live unwooed,
..... .. . lowly life to waste
The treasures of sweet ..........”
No. XXIV.--SHAKESPEARE’S MANTLE
Ingenious cryptic efforts have been made to prove that Bacon was the
author of Shakespeare’s plays, but it has been reserved for us to
reveal, by a convincing cryptogram, the modern wearer of his mantle.
The secret is disclosed by a line of capital letters shown below:--
Mac B eth.
Oth E llo.
Comedy of Er R ors.
Merchant of Ve N ice.
Coriol A nus.
Midsummer Night’s D R eam.
Merry Wives of Win D sor.
Measure for Mea S ure.
Much Ado about Not H ing.
Antony and Cleop A tra.
All’s Well that ends W ell.
41. MISSING WORDS
Till a man is as ----- of a ----- as his palm is,
We ----- him from earning his ----- in our armies.
The missing words are spelt with the same five letters.
42. THE PAUPER’S PLAINT
Pale penury that ------ social bands,
And any link that ------ worth to fame,
Take ye the blame for my inactive hands,
I ------ in vain to build upon the sands,
Without a ------ who can make a name?
The missing words are spelt with the same six letters.
No. XXV.--CAPITAL SHORT CUTS
The following example of the use of phonetic capitals and figures is
fresh and original. It contains more than eighty such symbols in its
twenty-four lines:--
A MAID OF ARCADY
A rosy maid of R K D
Is L N in her bower;
Brisk as U C A honey B,
And sweet as N E flower.
Does she S A herself 2 please
(XQQ the saucy miss),
She sings an L E G 2 TT,
Or blows an M T kiss.
“B mine, I say, U bonny J,
B 4 I CC mine L;
When you are gay my hopes D K,
In T sing U X L.”
Without ado she takes the Q,
Her II B 9 and B D,
“O, sir, I do not N V U
I C that U R C D.
“X S of spirits--O D V--
Begins 2 U U U up;
The cure must B a dish of T
With K N in the cup!”
“O L N U I C R true,
Y need I C Q less?
I’ll never D V 8 from U,
But end my cares with S.”
(_caress_).
43. MISSING WORDS
Mr Backslide, afflicted with weakness of mind,
-------- over to Lushington’s inn, where he dined.
He -------- the pledge he had taken as handy,
And emptied forthwith a -------- of brandy.
Each missing word has eight letters.
44
A ------ sat in his ------ grey,
Watching the moonbeams ------ play
On a keg that in the bushes lay,
And these were the words of his song:--
“Thou ------ the weak, thou ------ the strong,
To thee the ------ of bad deeds doth belong.”
And the leaves with a ------ took up the sad song.
Each of these missing words is spelt with the same six letters.
No. XXVI.--SIMPLE SCHOLARSHIP
Three hungry scholars came to a wayside inn, and saw this sign over the
door:
+-----------+
|PLACET ORE |
|STAT ORDINE|
|ORE STABIT |
|ORE AT ABIT|
+-----------+
One of them eager to show his ready wit, translated these Latin words of
welcome roughly into English verse:--
“Good cheer we provide,
Our service is sure;
Their savours abide
Though meats don’t endure!”
The complacent smile faded from his face as a village schoolboy, who had
overheard him, broke in with the real rendering of the words:--“Place to
rest at or dine; O rest a bit, or eat a bit!”
45
In these lines, where the dots occur, insert words, each of which is
longer by one letter than the one before, and so complete the poem. The
same letters are carried on each time in varied arrangement:--
Nature . love .. every land,
On burning plain, by wooded rill;
Where ... is girt by coral strand,
Or .... rears her castled hill.
Then ..... from me the tale to hear,
How, true to one ......, the bee
Once ....... out keeps, year by year,
The ........ by her instinct given,
Which teach her, wheresoe’er she roam,
In every clime beneath the heaven,
To build the same ......... home.
No. XXVII.--WAS IT VOLAPÜK?
| |
-+---------------+-
|FFAH CHTI WT |
|HGU ACT ONE|
|RASD RIB DLO|
-+---------------+-
| |
A schoolmaster in the Midlands, who was a bit of a wag, wrote this on
the blackboard, as a novel exercise for the boys of Standard VI. Can you
decipher it?
46
Here is another ingenious specimen of missing words, spelt each of them
with the same five letters:--
That Samson did a thousand -----
Is not so wondrous strange.
In days like these at ----- such feats
Assume a wider range.
The Press ----- news ----- now,
Enough to scare a sinner,
And any fool who chooses may,
In Samson’s way, his thousands slay
Who chews his ----- at dinner.
No. XXVIII.--ANOTHER EPITAPH
(_On an Old Pie Woman_)
BENE AT hint HEDU S.T.T.H. emo Uldy O
L.D.C. RUSTO F.N.E. L.L.B.
AC. hel orl AT Ely
W ASS hove N.W. how ASS Kill’d
Int heart SOF pi escu Star
D. sand Tart Sand K N ewe,
Ver yus E oft he ove N.W. Hens he
’Dliv’ Dlon geno
UG H.S. hem Ade he R la STP uffap
UF FBY HE RHU
S. B an D. M.
Uchp R.A. is ’D no Wheres He dot
H.L. i.e. TOM a Kead I.R.T.P. Iein hop est
Hat he R.C. Rust W I
L.L.B. ERA IS ’D----!
47. IN A FARM-YARD
All his flock from ------ rough,
To the ------ ran apace,
Where their ------, old and tough,
------, the guardian of his race.
In these lines each missing word is spelt with the same six letters.
48
This is a bright little specimen of a missing words puzzle:--
Come, landlord, fill the flowing ----
Until their ---- run over;
For in this ---- to-night I’ll ----,
To-morrow ---- to Dover!
Each missing word has the same four letters.
No. XXIX.--DOG LATIN
An old worn stone, with the inscription given below just legible, was
found near to some ancient Roman remains, and was the valued possession
of a local antiquarian, who was convinced that it dated back to the days
of the Emperor Claudius:--
BENE
AT . HTH . IS . ST
ONERE . POS . ET
H . CLAUD . COS. TERT
R . I . P
ES . ELLE . RO
F . IMP
IN . G . TONAS . DO
TH . HISCO
N . SORTJ
A . N . E
His pride of possession was, however, shattered when a rival collector
read it off into excellent English:--“Beneath this stone reposeth Claud
Coster, tripe seller, of Impington, as doth his consort Jane.”
49
Here, as quite a novelty, is a double-barrelled missing words puzzle. As
a puzzle, Part I. should stand alone, but the second part forms a
thinly-veiled solution, which throws light upon the missing words. These
are four in number and are spelt differently with the same six letters.
Part I
I tell of voices hushed and still,
I bid men prick their ears,
I help an army’s ranks to fill,
My gleam like gold appears.
Part II
Hushed is the still and ------ voice,
Pricked ears are keen to ------,
Men who ------ make noble choice.
------ like gold will glisten.
No. XXX.--THE PROBLEM SQUARED
P R O B L E M
R E C E I V E
O C T A V E S
B E A C O N S
L I V O N I A
E V E N I N G
M E S S A G E
This is a singularly perfect specimen of a seven-letter Word Square.
50. MISSING WORDS
Some men their -------- escorted on their way,
When “-------- look here!” I heard a driver say:
“It -------- our pluck to toil like -------- all day,
When wanting -------- we starve on wretched pay.”
Each missing word is spelt with the same five letters.
No. XXXI.--BY LEAPS AND BOUNDS
Can you disentangle the eight-line verse which is scattered over these
64 squares? You must leap always from square to square, as a knight
moves on the chess-board.
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| tle | to | a |cat- |life | and |live | In |
| | | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| By | tle | ow- |bro | of | non |tle |fall |
| | | |wse | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| ter |tur- | gain| like|land |one’s|quiet| And |
| | | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| of | ar | Bet-| me | and |Than | a- |bat- |
| | m | | ad- | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
|bask | Be | lau-| or | tle |ness |done |wan- |
| | t- | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| rel | let |Than |die |With | der | of | smo |
| | | | | | | | ke |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| ter | in |brain|myr- | on | and |har- | un- |
| | | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| Ch | or |to |sun |with |work | In |heat |
| ap- | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
The verses begin with “Better to die,” and end with “tle” in the top
left-hand corner.
51. WISDOM WHILE YOU WAIT
As a -------- -------- of facts you’ll find
Our Encyclopedia -------- the mind.
The three missing words are spelt with the same seven letters.
52. MISSING WORDS
You drink that --------, -------- wine, too lavishly at night,
And say a -------- or a swim next morning puts you right,
When night brings you a sudden --------, and morning devils blue,
Then you’ll ------ your careless boast, and own my warning true.
Each missing word is spelt with the same six letters.
No. XXXII.--A BROKEN SQUARE
Can you complete this broken Word Square?
+---------+
| |O| |E| |
+-+-+-+-+-+
|O| | | |E|
+-+-+-+-+-+
| |I| |O| |
+-+-+-+-+-+
|E| | | |E|
+-+-+-+-+-+
| |E| |E|-|
+-+-+-+-+-+
53
The missing words in these lines are all spelt with the same six
letters:--
--- -------- but for rebel act
Without --- -------- should be;
But this --- --- --- end, in fact
None find --- -------- in me.
54. MISSING WORDS
“Oh for a ----- in this vast solitude,
This endless rise and fall of ----- and moor!”
Soliloquised a ----- in sad mood,
As through the lonely hills the staff of life he bore.
Spelt with the same five letters.
No. XXXIII.--A KNIGHT’S TOUR PROVERB
If the letters on these squares are taken in proper sequence they will
form the words of a well-known proverb:--
+-+-+-+-+-+-+-+-+
| | | | | | | | |
+-+-+-+-+-+-+-+-+
| | | | |E| | | |
+-+-+-+-+-+-+-+-+
| | |E| | | |T| |
+-+-+-+-+-+-+-+-+
| | | |L|H| | | |
+-+-+-+-+-+-+-+-+
| |E| |R| |S| | |
+-+-+-+-+-+-+-+-+
| | |E|A|S| | | |
+-+-+-+-+-+-+-+-+
|D| |E| |O| |S| |
+-+-+-+-+-+-+-+-+
| | | |S|P| |M| |
+-+-+-+-+-+-+-+-+
When a starting point has been chosen for trial of this puzzle, the
successive letters must occupy the squares which in every case are
reached by a knight’s move at chess, until a popular proverb is formed.
55. “MONSTRUM HORRENDUM INFORME INGENS”
’Twas in ........ that we saw him play
Like a ........ in his sports, and they
Amuse us as a good ........ may.
Each missing word has the same eight letters.
No. XXXIV.--GUARINI’S PROBLEM