## Sum Talk Of Alexander

Effect: Someone is asked to write down any number between one and ten. The performer writes a second digit beside this, forming a two-digit number. This done, the spectator cuts roughly half the cards from a shuffled deck. Both spectator and performer shuffle their halves; then the spectator pulls any card he likes from his half and lays it face-up on the table.

The performer reunites the halves of the pack and, without altering the order of the cards, deals onto the table a number of cards equal to the value of the selection. The last card of the count is turned up and placed with the spectator's card. Then the value of this new card is counted off and the last card of the count turned up. This card is placed with the first two cards, and its value is used to count down In the pack. The procedure is continued until the entire pack has been exhausted.

Now the spectator is instructed to add up the values of the random cards turned up during the deal. That value, strange as it seems, exactly matches the two-digit number chosen in the beginning.

Method: Mr. Elmsley's title offers a clue to the parentage of this trick. The Alexander referenced is not he of Macedonia, nor of Elmsley, but of Kraus. In Ibidem, Nos. 12 and 13, Alexander F. Kraus contributed a card puzzle with a fascinating mathematical solution. Further ideas by Tom Ransom and Max Katz were appended to Mr, Kraus' article. The trick described above is the fruit of Mr. Elmsley's dalliance with this mathematical oddity and the groundwork in its application contributed by the puzzling minds of these three men.

A simple setup is responsible for this curious coincidence effect. You must have a full deck of fifty-two cardsâ€”no jokers. Remove a set of ten cards, the values of which run from ace through ten. The suits should be mixed. Arrange these cards in descending order, with the ace at the face of the packet. Place any nine spot beneath the ace and place these eleven cards on the bottom of the deck.

In performance, give the pack a quick overhand shuffle, retaining the bottom stock. Then set down the cards and hand a pencil and slip of paper to someone. Ask that she write down any number between one and ten. If she by chance selects five, have her write down a second digit after it, creating a random two-digit number. If, however, her first choice is something other than five, take the pencil from her and write five before her digit, assuring that a number from fifty-two to fifty-nine is formed. Mentally subtract the spectator's chosen digit (i.e., the units digit of the two-digit number) from ten and remember the result. For example, if the spectator chose three, and the number fifty-three has been formed, subtract three from ten, leaving seven. Seven then becomes your key number.

Have the spectator cut off roughly half the pack. Pick up the bottom half for yourself and ask her to shuffle her cards, indicating through your own actions an overhand shuffle. Your explanatory shuffle consists of nothing more than a quick run of a few cards. Run a number of cards equal to your key number from the top of the packet to the bottom. Do not disturb the eleven-card setup as you do this. You can, if you like, follow this shuffle adjustment with a brief false shuffle, as the spectator shuffles her portion.

When the mixing has been completed, have her remove any card she wishes from her group and lay it face-up on the table. Retrieve the balance of her packet from her and set it onto your own.

Point out the value of the random card she has chosen (all court cards are given a value of ten) and deal that number of cards, counting them aloud, into a face-down pile. Turn up the last card of the count and lay It onto hers. Draw attention to the value of this chance card and count an equal number from the pack, dealing the cards onto the existing pile on the table. Turn up the last card and place It with the previous two. Continue counting and turning up cards in this fashion until you can go no further; that is. until there are not enough cards left in the talon to count the value of the final card. That last face-up car d, by the way, will always be the nine at the bottom of your setup.

If you now add the values of all the cards set aside during the deal, their total will equal the two-digit number constructed at the beginning of the trick.

You can allow the spectator to do the dealing, thus eliminating any suspicion of sleight-of-hand on your part. However, if you choose this course, you must make your instructions extremely clear or confusion and possible failure will result.

The selection procedure can be handled in another way. Rather than have the spectator cut off half the pack and shuffle it, simply give the cards a casual shuffle yourself, transferring the necessary number of cards from top to bottom. Then fan out the top half of the pack for a selection to be made. The card, of course, cannot be drawn from the setup or from those cards below it. Do not, however, sell short the impression of fairness lent by the spectator's shuffling in the original handling. Though she is permitted to shuffle only half the deck, this counts for more in the audience's perception than your shuffling of the entire pack.

Since the final card turned up will always be the bottom card of the setup, some will be tempted to tack on a supplementary effect in which they predict that card. This is certainly possible, but predicting the card may seem too pat to an audience, and can undermine the effect as a whole. In this case, as In so many others, less may well be more.

It will be understood that the spectator's selection is limited to a number betiueen one and ten as this ensures a single digit other than one. One is avoided because it requires a shift of nine cards to the bottom of the pack, which would deny you the option of stopping at the nine on the face of the setup, thus adding one more card to the total and upsetting the desired sum. Mr. Elmsley has worked out two solutions that allow one to be included in the selection range:

1) If one is chosen by the spectator, palm away one or two cards from the bottom of the pack before you begin to deal through it. The palmed cards will have to be secretly disposed of In a pocket or the lap.

2) Make the bottom card of your setup a ten instead of a nine, and secretly remove two cards from the pack before you begin, leaving fifty. If you then subtract the chosen digit from nine instead of ten, you will arrive at the number of cards you need to transfer from top to bottom with your shuffling.

Although these alternatives are reasonably efficient, I think most performers will prefer the original ploy of simply eliminating one from the selection bank through subtle phrasing.

The setup exploited here automatically forces a total of sixty when no shuffle displacement is performed. By transferring cards under the setup, you reduce the total by that number of cards. If you replace the nine at the bottom of the setup with a card of another value, the base total is changed.

An ace yields a total of fifty-two;

a two gives fifty-three;

a three gives fifty-four;

a four gives fifty-five;

a five gives fifty-six;

a six gives fifty-seven; a seven gives fifty-eight; an eight gives fifty-nine;

and a ten or a court card (counting as ten) yields sixty-one, One other interesting fact about the construction of this stack should be mentioned. The descending ten-through-ace sequence that sits above the final card of the stock need not be strictly adhered to. Any value in that sequence may be replaced with a ioujer value and the stack will still function. For example, a stack reading eight-four-six-seven-two-three-four-two-two-ace from top to bottom will still deliver the desired eleventh card of the stock. Given this information, you can arrange the stack quite rapidly.

It will be obvious that this setup can be useful for forcing any number from fifty to sixty-one. Study of this system can, I'm certain, lead to other interesting uses as well.

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