10 Dice

Suppose that 10 10 dice are rolled. Each die is a regular 6 6 -sided die with numbers 1 1 through 6 6 labelled on the sides. How many different distinct sums of all 10 numbers are possible?

Details and assumptions

The sums 5 = 1 + 4 5 = 1+4 and 5 = 2 + 3 5 = 2 + 3 are the same sum (namely 5), and should only be counted once.


The answer is 51.

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