THE WIZARD’S POCKETBOOK

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.

Fig. 37

Fig. 38

Fig. 39

Fig. 40

Fig. 41

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:

This order may be instantly recalled by using as a memory-peg the word CHaSeD, 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:

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 1Key Number1
” 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:

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.