A Dice Puzzle

Timothy and Urban are playing a game with two six-sided dice. The dice are unusual: Rather than bearing a number, each face is painted either red or blue.

The two take turns throwing the dice. Timothy wins if the two top faces are the same color, and Urban wins if they’re different. Their chances of winning are equal.

The first die has 5 red faces and 1 blue face. What are the colors on the second die?

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Throwing two six-sided dice produces 36 possible outcomes. If Timothy and Urban have equal chances of winning, then there must be 18 outcomes in which both dice display the same color. If x is the number of red faces on the second die, then: 18 = 5x + 1(6 – x) x = 3 The second die must have 3 red faces and 3 blue faces. (From Pierre Berloquin, 100 Numerical Games, 1994.)

October 23, 2014November 3, 2014 | Puzzles · Science & Math