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Problem 240


Problem 240


Top Dice

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?


点数最大的骰子

扔出5个六面骰子(面上分别标有1至6),其中三个最大的点数之和为15,一共有1111种方式。其中的一些例子为:

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

扔出12个12面骰子(面上分别标有1至12),其中十个最大的点数之和为70,一共有多少种方式?