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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