a) I have a pair of fair n-sided dice. The probability when both are rolled that their results differ by two is the same as that the sum will be 5 or less. Find n.

b) I have two dice, one with n sides and the other with m sides. When they are rolled the probability they are equal is the same as that they sum to 13 or higher. Find n and m.

c) I have a trio of n-sided dice. When I roll them all the probability that the dice all show different numbers is greater than when they sum 15 or less but less than when they sum 16 or less. Find n.

Note: "x sided dice" are numbered with consecutive integers from 1 to x.

a) 7

b) {1,12}, {3,11}, {6,9}
  assuming n < m, n = sum of first k #s for some k and m=12-n+k
for k = 1,2, 3 m>n and solution is above
for k>=4 m<n

c) 6

Posted by Joel on 2006-11-30 13:18:02