2. Fifteen numbers are arranged in a circle. The sum of any six consecutive numbers is 50. Petya covered one of the numbers with a card. The two numbers adjacent to the card are 7 and 10. What number is under the card?
Answer: 8.

Solution. Let the number at the $i$-th position be $a_{i}(i=1, \ldots, 15$.) Fix 5 consecutive numbers. The numbers to the left and right of this quintet must match. Therefore, $a_{i}=a_{i+6}$. Let's go in a circle, marking the same numbers:

$$
a_{1}=a_{7}=a_{13}=a_{4}=a_{10}=a_{1} .
$$

Now it is clear that for any $i$, $a_{i}=a_{i+3}$, i.e., the numbers go in the following order:

$$
a, b, c, a, b, c, \ldots, a, b, c
$$

From the condition, it follows that

$$
2(a+b+c)=50
$$

Thus, the sum of any three consecutive numbers is 25. Hence the answer.

Scoring. 12 points for a complete solution.