10. There are two symmetrical dice. Can the numbers on their faces be written in such a way that the sum of the points when rolled takes the values $1,2, \ldots, 36$ with equal probabilities

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# Solution.

Let's provide an example of such dice. Suppose the first die has the numbers 1, 2, $3, 4, 5, 6$, and the second die has $0, 6, 12, 18, 24, 30$. Notice that any number from 1 to 36 can be uniquely represented as the sum of numbers written on the two dice. Thus, the sum of the points when rolling the dice takes the values $1, 2, \ldots, 36$ with equal probabilities.

Answer: Yes, it is possible.