Nontransitive Dice
Consider
three six-sided dice A, B, and C, with the following numbers on their sides:
A: 2, 2, 4, 4, 9, 9
B: 1, 1, 6, 6, 8, 8
C: 3, 3, 5, 5, 7, 7
What
is the probability that:
· A produces a higher number than B?
· B produces a higher number than C?
· C produces a higher number than A?
Can
you find another set of face values for A, B, and C that yield the same
properties? (Does such a set even exist?)
This brainteaser was
written by Derrick Niederman.