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Top Dice

Problem 240

Published on Friday, 10th April 2009, 10:00 pm; Solved by 1369

There are 1111 ways in which five 6-sided dice (sides numbered 1 to 6) can be rolled so that the top three sum to 15. Some examples are:

D1,D2,D3,D4,D5 = 4,3,6,3,5
D1,D2,D3,D4,D5 = 4,3,3,5,6
D1,D2,D3,D4,D5 = 3,3,3,6,6
D1,D2,D3,D4,D5 = 6,6,3,3,3

In how many ways can twenty 12-sided dice (sides numbered 1 to 12) be rolled so that the top ten sum to 70?