# 10 Dice

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

Details and assumptions

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

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