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Problem of the Week 957

A Tie Game?

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This week's problem is a simple variation on a children's game. The game involves two players, each with a single six-sided die, and list of the integers 1-6 (used to record their rolls). The object of the game is to maximize the sum of six rolls of the die. The players alternate rolling, and they add the roll of the die to their total if they have not used that roll yet (in other words if a player rolls 6, 5, 6, 5, 3, 6, then their total is 14, since they can count only the first occurrence of each roll). The maximum possible score is 21 (when each roll occurs exactly once in the six rolls), and the minimum possible score is 1 (each roll is a 1).

What is the probability the game ends in a tie?

SOURCE: Dan O'Loughlin, Macalester College.

© Copyright 2002 Stan Wagon. Reproduced with permission.

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20 March 2002