“HOW WOULD YOU----?”
PUZZLES THAT PLEASE
HISTORY records that the blind poet Homer lost his reason in a vain
endeavor to solve a riddle, and from his days until these present times
much care and thought have been expended in the invention of puzzles
both difficult and simple. It is the object of this chapter to present
the reader with a few simple ones.
Two easy and yet fascinating puzzles can be worked with an ordinary
checker-board.
1. THE TRAVELING CHECKER
Place a checker upon a square near the center of the board, as in Fig.
1. In how few moves can you make it traverse every square in the board
and return to its starting-point?
[Illustration: FIG. 1.--The traveling checker.]
[Illustration: FIG. 2.--Joining the rings.]
2. ANOTHER CHECKER PUZZLE
Place sixteen men on a checker-board in such a manner that no three men
shall be in a line, either horizontally or perpendicularly.
3. JOINING THE RINGS
Nine rings are connected by six straight lines, as shown in Fig. 2.
Connect these same nine rings by four straight lines.
4. THE TEN ROWS
This is a puzzle with nine checkers or counters. Dispose these counters
in such a manner that ten rows are formed with three men in each row.
[Illustration: FIG. 3.--The cabalistic sign.]
5. THE CABALISTIC SIGN
Fig. 3 shows a piece of paper cut into a famous cabalistic sign. How can
you divide it into four pieces which, placed together, shall form a
square?
6. THE DANGEROUS ANARCHISTS
Once upon a time there were eight anarchists confined in separate cells
connected by the system of passages shown in Fig. 4. The prisoners, each
of whom had his own number, occupied cells in the order shown.
One day the governor of the jail decided that his prisoners should be
transferred from one cell to another in order that their numbers should
run consecutively from left to right. Accordingly he gave orders for
this to be done, but at the same time directed his warders that on no
account were any two prisoners to meet, either in the passages or cells.
As there was only one vacant cell at their disposal, how did the warders
work this maneuver successfully?
[Illustration: FIG. 4.--The dangerous anarchists.]
You will find the best way to solve this problem is to draw a plan
similar to that shown in Fig. 4, and place eight numbered counters in
the respective cells.
7. CATCHING THE DONKEY
A man once wanted to saddle a donkey, and proceeded, bridle in hand, to
the field where Ned was feeding.
Let Fig. 5 represent the field, which the man entered by the gate at 63,
whilst the ass was standing in the opposite corner at 2.
Now you can move either the man or the donkey to any number in the
straight line, but neither must cross or rest upon a line covered by the
other. For instance, if the donkey be at 2, the man can move to 62, 61,
59, 36, or 13; but he cannot go to either 60 or to 5, for then the
donkey would gallop up and let fly with his heels. Ned, on the other
hand, can go to 6, 28, 51, 3, or 4, but if he were to go to 60 or 5 the
man at 63 would catch him at once.
[Illustration: FIG. 5.--Catching the donkey.]
Giving the donkey the first move, how soon can you place the man in such
a position that the ass is cornered and cannot escape being bridled?
8. LIKE TO LIKE
[Illustration: FIG. 6.--“Like to like.”]
Four black and four white counters are placed alternately in a row of
ten divisions, shown in Fig. 6. By moving two at a time, how can you
arrange all the blacks and all the whites together in four moves?
9. THE BROKEN CHAIN
A lady once took to a jeweler a gold chain, broken into five pieces of
three links each (Fig. 7). She asked him to repair the chain, agreeing
to pay 25 cents for each link that he had to break and weld in order to
restore the chain to its original length.
The following day she sent her maid for the chain with 75 cents. If you
had been the jeweler, how would you have mended this chain of five
pieces by breaking only three links?
[Illustration: FIG. 7.--The broken chain.]
10. THE DIAMOND CROSS
The same lady wished to have a diamond cross reset, and pleased with the
intelligence shown by the jeweler, she decided to give him the work.
[Illustration: FIG. 8.--The diamond cross.]
But she was determined to give him no opportunity of cheating her, so
she counted the stones from top to bottom (Fig. 8), and found there were
nine. She then counted them from the bottom to the extremity of each arm
of the cross, and found that they also numbered nine. Having noted these
figures, she sent the cross to be reset.
But the jeweler was a crafty man, and knowing how she had reckoned the
diamonds, he stole two, and having reset the remainder, he returned the
finished piece of work.
When she received her cross, the lady thought it looked rather
different, and counted the stones according to her former plan. The
numbers were exact! So she paid the jeweler, who went off smiling.
How had he managed the theft?
11. THE QUARRELSOME RAILWAYS
Five competing railway companies decided to place termini in a certain
small town. But land was dear; and after much negotiation they were able
to secure sites only as shown in Fig. 9.
But none of the companies would grant any of its competitors running
powers over its lines, and as the municipal authorities decided that all
five lines should enter the city side by side, the engineers found
themselves confronted with the following problem:--How is each line to
reach its destination, without crossing any of its competitor’s tracks?
How would you extricate them from this dilemma?
[Illustration: FIG. 9.--The quarrelsome railways.]
12. ANOTHER RAILWAY PROBLEM
This problem is shown in Fig. 10. In the railway A, B, C there are two
sidings, A, D and C, E; which meet at F. At this latter place there is
only sufficient space to contain one car of the size of G or H, and
there is no room for the engine, I. Consequently, if this engine is sent
up either of the sidings it must return by the same tracks.
[Illustration: FIG. 10.--The second railway problem.]
The point to be discovered is: How can the engine, I, transpose the two
cars G and H, by simply using the rails shown in the illustration?
13. THE MITER
Study Fig. 11 closely, and think how you can divide a piece of paper
thus shaped into four similar parts.
[Illustration: FIG. 11.--The miter.]
SOLUTIONS
1. _The Traveling Checker_
You cannot make the checker traverse all the squares in less than
sixteen moves, as shown in Fig. 12.
[Illustration: FIG. 12.--Solution to traveling checker.]
[Illustration: FIG. 13.--Solution to second checker puzzle.]
2. _Another Checker Puzzle_
The way to place the sixteen pieces so that no three are in a line in
any direction, can be seen from Fig. 13.
3. _The Rings Joined_
The nine rings can be joined by four lines, as shown in Fig. 14.
[Illustration: FIG. 14.--The joined rings.]
4. _The Ten Rows_
The complicated geometrical figure shown in Fig. 15 shows the ten rows
formed with nine counters.
5. _The Cabalistic Sign_
By making the two cuts shown in Fig. 16, the piece of paper will be
divided into four parts that will fit together into a square.
[Illustration: FIG. 15.--The ten rows.]
[Illustration: FIG. 16.--Solution to cabalistic sign puzzle.]
6. _The Dangerous Anarchists_
The simplest method of rearranging the prisoners was as follows (as
there was only one vacant cell at any time the numbers designate which
prisoner was moved therein)--1, 2, 3, 1, 2, 6, 5, 3, 1, 2, 6, 5, 3, 1,
2, 4, 8, 7, 1, 2, 4, 8, 7, 4, 5, 6.
7. _Catching the Donkey_
According to the rules of the game, the donkey moves first, and the
following is one of the shortest methods by which the man can catch him.
It will doubtless amuse you to find other, and probably quicker ways of
cornering Ned.
Donkey to 3
Man „ 36
Don. „ 21
Man „ 30
Don. „ 3
Man „ 8
Don. „ 4
Man „ 7
Don. „ 5
Man „ 12
When the man has driven the ass into the corner at 5, of course there is
no more chance of escape, and Ned has to submit to the bridle with
resignation.
8. _Like to Like_
Moving two men at a time, the four moves are:--
2 and 3 moved to spaces 9 and 10
5 „ 6 „ „ 2 „ 3
8 „ 9 „ „ 5 „ 6
1 „ 2 „ „ 8 „ 9
The counters will then appear as in Fig. 17.
[Illustration: FIG. 17.--Solution to “Like to like” puzzle.]
9. _The Broken Chain_
To repair the chain the jeweler had recourse to a very simple device.
Breaking the three links of one of the pieces he used them to join the
remaining four pieces, thus restoring it to the original length.
10. _The Diamond Cross_
The owner of the diamond cross thought she had been very clever in
counting the stones as she did, but her cunning overreached itself, for
the jeweler had only to remove the diamonds of the extremities of the
cross-piece, and shift this latter up one point, as in Fig. 18, to make
his theft almost unnoticeable. You will find the diamonds count nine,
even though two stones have been removed.
[Illustration: FIG. 18.--Solution to diamond cross puzzle.]
[Illustration: FIG. 19.--Solution to the quarrelsome railways puzzle.]
[Illustration: FIG. 20.--Solution to miter puzzle.]
11. _The Quarrelsome Railways_
After much surveying and discussion, the railways laid their lines as
shown in Fig. 19.
12. _The Other Railway Problem_
The following is the simplest method by which the engine could transpose
the cars G, H.
I pushes G into F, and returns and pushes H up to G. The two cars are
then coupled together, drawn down to C and pushed over to A. G is then
uncoupled, and I takes H back to F and leaves it there. I then returns
to G, pulls it back to E and leaves it there. I then returns to H by way
of C, and draws it down to D, thus completing the task.
13. _The Miter_
A glance at Fig. 20 will show how the miter can be divided into four
similar parts.