This is an extremely small volume, consisting in fact of six pages only,
and no letterpress, the instructions for its use being embodied in a
separate leaflet. On each of its pages are miniature reproductions of
thirty-six playing cards, six in a row; every card of the pack being
represented once at least among the whole number. The object of the book
is to enable the owner to discover the name of a card drawn (or merely
thought of) by some member of the company. The chooser is only asked to
look at the book, and state on which one or more of its pages the card
in question appears, when the performer, without seeing or handling the
book himself, can instantly name the card. The six pages of the book are
reproduced in the diagrams which follow. Figs. 37-42.
[Illustration: FIG. 37]
[Illustration: FIG. 38]
[Illustration: FIG. 39]
[Illustration: FIG. 40]
[Illustration: FIG. 41]
[Illustration: FIG. 42]
To be in a position to work the trick, it is necessary in the first
place to memorise each of the fifty-two cards of the pack in connection
with a particular number. This may at first sight appear a formidable
undertaking, but it is not so in reality.
All that really needs to be memorised is the order of the suits; which is
as under:
1. Clubs.
2. Hearts.
3. Spades.
4. Diamonds.
This order may be instantly recalled by using as a memory-peg the
word _CH_a_S_e_D_, which contains the initials of the four suits in
the proper order, or the reader may if he prefers it recall them by
reflecting that _Cool Heads Soon Decide_.
The arrangement of each suit follows the natural order, the ace of clubs
being No. 1; the deuce 2; and the trey 3; knave 11; queen 12 and king 13.
The card next following, viz., the ace of hearts, will be 14; the deuce
of hearts 15, and so on, the complete arrangement being as shown below:
1. Ace of clubs.
2. Deuce of clubs.
3. Trey of clubs.
4. Four of clubs.
5. Five of clubs.
6. Six of clubs.
7. Seven of clubs.
8. Eight of clubs.
9. Nine of clubs.
10. Ten of clubs.
11. Knave of clubs.
12. Queen of clubs.
13. King of clubs.
14. Ace of hearts.
15. Deuce of hearts.
16. Trey of hearts.
17. Four of hearts.
18. Five of hearts.
19. Six of hearts.
20. Seven of hearts.
21. Eight of hearts.
22. Nine of hearts.
23. Ten of hearts.
24. Knave of hearts.
25. Queen of hearts.
26. King of hearts.
27. Ace of spades.
28. Deuce of spades.
29. Trey of spades.
30. Four of spades.
31. Five of spades.
32. Six of spades.
33. Seven of spades.
34. Eight of spades.
35. Nine of spades.
36. Ten of spades.
37. Knave of spades.
38. Queen of spades.
39. King of spades.
40. Ace of diamonds.
41. Deuce of diamonds.
42. Trey of diamonds.
43. Four of diamonds.
44. Five of diamonds.
45. Six of diamonds.
46. Seven of diamonds.
47. Eight of diamonds.
48. Nine of diamonds.
49. Ten of diamonds.
50. Knave of diamonds,
51. Queen of diamonds.
52. King of diamonds.
The arrangement of the table being once understood, the number associated
with any given card in the club suit suggests itself automatically,
_e.g._, the seven of clubs is likewise No. 7 in the list. To ascertain
the name of the card corresponding to any of the higher numbers, all that
is needed is to subtract from that number 13, or such higher multiple of
thirteen as the case will admit, and the difference will represent its
position in its own suit.
Suppose, for instance, that the performer desires to know what card
answers to the number 20. Deducting thirteen from 20, the remainder, 7,
tells him that the card is the seventh (_i.e._ the seven) of the second
suit, viz., hearts. If he wants to know the name of No. 29, he deducts
26, when the remainder, 3, tells him that the card is the three of the
third suit, spades. If the card be No. 40, the number to be deducted
will be 39, and the remainder, 1, tells him that the card is the first
of the fourth suit, viz., the ace of diamonds. After a very few trials,
this little exercise in mental arithmetic becomes so familiar that the
calculation becomes practically instantaneous.
Going a step further; with each of the six pages of the pocket-book is
associated a special number, known as its “key” number. These are as
under:
Page 1 Key Number 1
” 2 ” ” 2
” 3 ” ” 4
” 4 ” ” 8
” 5 ” ” 16
” 6 ” ” 32
The memorising of these is also a very simple matter, for it will be
noted that the key numbers are the first six factors of the familiar
geometrical progression, 1, 2, 4, 8, 16, 32. Printed as below:
1, 2, 3, 4, 5, 6
---------------------
1, 2, 4, 8, 16, 32
the upper figures, in ordinary type, expressing the numbers of the pages,
and the lower, in black type, the corresponding key numbers, a very small
amount of study will associate them so closely in the mind as to fix them
firmly in the memory.
Having mastered these two simple lessons, the learner is in a position
to use the pocket-book. To ascertain the card chosen, he has only to add
together the key numbers of the pages in which he is told that such card
appears. The total will be the number at which that card stands in the
list given on page 185, and, this being known, it becomes an easy matter
to name the card itself.
We will suppose, for instance, that performer is told that the chosen
card appears on the second page, and no other. The key number of this
page being 2, the card must be the second in the list, viz., the deuce
of clubs. If he is told that the chosen card is to be found on pages 1,
3 and 6: the key number of these three pages being 1, 4 and 32: together
making 37, and thirty-seven less twenty-six being eleven, he knows that
the card must be the eleventh of the third suit, otherwise the knave of
spades. If he is told that the card is on the third, fifth and sixth
pages, the key numbers of which are 4, 16 and 32, total 52, it is clear
that the card must be the last in the list, viz., the king of diamonds.
* * * * *
So much for the working of the trick. But the reader, if of an enquiring
mind, will naturally ask, “How is this result obtained?” The answer
rests upon a special property of the geometrical progression which forms
the six key numbers. It is a curious fact that by the use of these six
numbers, either singly or in combination with others of the series, any
number, from unity up to 63, can be expressed. Thus, the numbers, 1, 2,
4, 8, 16 and 32 we already have, these being numbers of the series. As to
other numbers:
1 + 2 = 3
4 + 1 = 5
4 + 2 = 6
4 + 2 + 1 = 7
8 + 1 = 9
8 + 2 = 10
8 + 2 + 1 = 11
8 + 4 = 12
8 + 4 + 1 = 13
and so on throughout up to 52, which being the limit of the pack, is the
highest number with which we need concern ourselves.
In making up the pages of the pocket-book, advantage has been taken of
this principle. A given card is inserted on that page or pages (and those
only) whose key numbers, alone or added together, correspond with the
position which the card holds in the list. Thus the ace of clubs will
appear on the first page (not because it is the first card, but because
the key number of that page is 1) and on no other. The deuce of clubs,
in like manner, on page 2, the key number of that card being two. The
next card, the three of clubs, must appear on page 1 and page 2, their
key numbers together amounting to 3. The process as to cards standing
at higher numbers is the same. Thus, the ace of spades, being the
twenty-seventh card, and twenty-seven being the aggregate of 16, 8, 2 and
1, will appear on the first, second, fourth and fifth pages. Conversely,
if the performer is told that the card appears on the four pages last
named, he knows that it is the twenty-seventh card, _i.e._, the ace of
spades. Any spaces remaining vacant on the page after the whole pack has
been dealt with, are filled up by duplicates of cards already figuring
_on the same page_, their appearing under these conditions making no
difference to the calculation.
I am indebted to an ingenious amateur, Mr. Victor Farrelly, for the
idea of a novel method of using the pocket-book. Mr. Farrelly does not
offer of his own accord to show what can be done with it, but keeps it
in reserve, for use in a special emergency. Every conjurer meets now and
then with the pig-headed person who absolutely declines to have a given
card forced upon him, and persists in endeavouring to extract one from
some other part of the pack. Armed with the pocket-book, the performer
can set such a person at defiance, and indeed get additional _kudos_ from
his objectionable behaviour.
He cheerfully gives up the struggle, saying “You seem to think, sir,
that I wish to influence your choice in some way. To prove the contrary,
I give the pack into your own hands. Shuffle it well. Thank you. Now
take from it any card you please. Look at it, and put it in your pocket.
You are satisfied, I presume, that I do not know that card? You are
quite right. I have not the smallest idea of it, but I shall discover
it without the smallest difficulty by a process of mathematical magic.
I have here” (producing pocket-book) “a little book of six pages, on
each of which thirty-six cards are illustrated. Will you kindly see
whether the card you chose is represented among those on the first page?
Meanwhile I will divide the pack, which please remember I have not
touched since you shuffled it yourself, into six portions, one for each
page of the book.” This is done, the six packets being turned face down
on the table.
We will suppose that the chosen card is not found on the first page.
“Then,” says the performer, “this first packet will tell me nothing, and
may be disregarded. Now, for the second page, is your card upon that? It
is? Then I draw two cards from the second heap, and turn up one of them.
And now for the third page. Do you find your card there? You do? Then I
take up three cards from the third packet, and again turn up the last
one.”
We will suppose that the chosen card is not found in either the fourth
or the fifth page, but re-appears on the sixth, whereupon six cards are
counted off from the corresponding packet, and the last of them turned
up. The performer has by this time mentally added up the key numbers of
the second, third and sixth pages: viz., 2, 4 and 32, together making 38,
and knows therefrom that the card is the thirty-eighth in the list, viz.,
the queen of spades. He does not however at once display his knowledge,
but pretends to make a mental calculation from the cards exposed upon the
table, giving, if he so pleases, and the cards lend themselves to it,
some fanciful explanation of his method. It seems to me, however, that
this last is a needless elaboration. Personally, I should prefer merely
to call attention by name to the cards exposed, and say, “When these
three cards appear in conjunction, it is clear that the card drawn was
the queen of spades” (or whatever it may happen to be). Any one deluded,
as the majority will probably be, into believing that you really infer
the name of the drawn card from those on the table, will be farther from
the real solution than ever.