Experimental Gambling System
Dean S. Clark, Stanford S. Bonan · Mathematics Magazine · 1987
After emphasizing point (3), Duval instructs the audience to begin the experiment by writing the numbers 1 to 13 arbitrarily around the circle, one number in each of the thirteen positions. This is to be done privately and according to your own whim-the more random the better. Duval says that those who have disobeyed and written 1 to 13 in the natural order will be among those choosing to withdraw from the game once the rest of the rules are announced. The next step is to compute the largest sum given by three consecutive numbers in the circular arrangement. This sum is a player's secret number. It is confidential and unalterable. Accuracy is a must here, since the winner will evidently have to authenticate his or her secret number. The audience gets busy computing and double-checking their secret numbers. You have written