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The Futurist Veteran user 331 Posts |
A modular inverse of the number y (mod x) is the number, that when multiplied by y, turns out to be 1 mod x: ie) the remainder when the product is divided by x equals one. When x is a prime number we are guaranteed x-1 such modular inverses.
So, a freely-chosen number from column A multiplied by its counterpart in column B will equal 1 (mod 13). A B 1 1 2 7 3 9 4 10 5 8 6 11 7 2 8 5 9 3 10 4 11 6 12 12 The following, off the top of my head, may not be the best trick in the world, but I'm just exploring the idea! Maybe someone can come up with a very clever trick using this principle, or has already done so. Have an Ace at positions 1, 14, 27 and 40 in the deck. Moreover, the first 12 cards of the deck are A,7,9,10,8,J,2,5,3,4,6,Q of whatever suit. The rest of the cards are as random as you like and should pass muster if looked at by the spectator. False shuffle and false cut if you like, and ask the spectator to pick a number between 1 and 12. Deal down to that card and say, "Well, we'll use the number on that card, multiply it with your original number, and start again, dealing down to that card in the deck." Naturally, Jacks count as eleven, Queens as twelve. If the resulting number is over 52 (if their original choice of number was 6, 11 or 12), explain that you have to deal the entire deck out & start again from the top, except you don't actually have to do that if you explain the procedure with clarity. This might make it look a bit fair and 'random', and not like you forced the numbers to be constrained to less than 52. They will inevitably reach an Ace by this procedure, which you can milk in your preferred 'prediction' manner. |
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