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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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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 $0,6,12,18, 24, 30$. Any number from 1 to 36 can be uniquely represented as the sum of the 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

It is possible.