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Possibly the greatest mathematical card trick ever!

Sixteen playing cards are dealt face up forming a 4x4 array, like this:

I now write a note in which I identify the card, including the suit, which will appear at the
end of the trick. This note is folded up and put aside for the moment.

Choose any four of the above cards, no two of which are in the same row and no two of which are in the same column. Using the values ace = 1, jack = 11, queen = 12 and king = 13, add up the values of your four chosen cards and call the sum S. Ask yourself: On an ordinary clock, what time would it be S hours after midnight?

This is a number from 1 to 12. Possibly, this number is among the 16 cards originally dealt, above. If it is, imagine pulling it out of the array - it is your Magic Card, the one I wrote on the note at the beginning of this paragraph. It is the 7 of hearts (there is only one 7 in the above array, actually the 7 of hearts). If this prediction is incorrect, please scroll down to the Appendix, below, which also explains how, in practice, the chooser can be forced to select 4 cards, no two of which are in the same row or column.

Now, for instructions on how to design your own array to stack in advance at the top of the deck, see below. You'll be changing the entries in the list TopRow and the values of A, B and C.

No support for LM Objects

You have seven degrees of freedom: the four cards to choose as the TopRow of your array and three arbitrary (positive or negative) integers A, B and C. It should be emphasized that A, B and C are not necessarily card values, but the entries in TopRow are. Highlight the values of any of these, above, and change them. Please use lower-case letters for face cards. The prediction of the Magic Card, above, will always be correct, unless you get a message that your array is not "good", in which case the trick cannot be performed with those sixteen cards. The primary objective is to create a "good" array that looks suitably "random". The other - equally important - objective is to figure out how the arrays are generated from TopRow and A, B and C.

Appendix. If the prediction is incorrect, then one of three things happened: (i) two cards were chosen in the same row or in the same column; (ii) the four cards were added incorrectly; or (iii) S is correct, but the clock time S hours after midnight was computed incorrectly.

In practice, choosing the four cards could be accomplished by first turning over a single card in place, and then removing the other cards in the same row and column as the chosen card, putting them aside. From the remaining array a second card would be turned over, and the other cards in the same row and column as this second chosen card would be removed to one side. The process would be repeated two more times. In the end there are 4 face down cards, no two of which are in the same row or in the same column.

Original mathematical design 2003 by Dean Clark