Problem of the Week 797:
Weird Dice
Roll two ordinary dice and look at the sum of the numbers rolled. The
number of ways of getting a sum equal to 2 is 1 (1+1). The number
of ways of rolling a sum equal to 3 is two (1+2 and 2+1). The
number of ways of rolling a sum equal to 4 is three (1+3, 3+1,
2+2), and so forth until the largest possible sum which is 12 and
can only occur in one way (6+6).
Do there exist other pairs of 6 sided dice such that
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Every side has a positive number of dots.
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The set of dots on each die is not a permutation of the ordinary die,
i.e., is not {1,2,3,4,5,6} in some order.
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The number of ways of rolling a sum with the other pair of dice is the
same as the number of ways of rolling a sum with the ordinary dice, as
explained above.
Back to the Fall 1995 PotW Archive.
© Copyright 1996 Stan Wagon. Reproduced with permission.
Jeff Erickson
(jeffe@cs.berkeley.edu)
Last update: 23 Feb 96