2. The numbers from 1 to 8 are arranged in a circle. A number is called large if it is greater than its neighbors, and small if it is less than its neighbors. Each number in the arrangement is either large or small. What is the greatest possible sum of the small numbers?
Answer: 13.

Instructions. Adjacent numbers cannot be of the same type, so large and small numbers alternate, and there are four of each. 8 is large. 7 is also large, since a small number must be less than two numbers, and seven is less than only one. 1 and 2 are small. 6 and 5 cannot both be small, as they are less than only two numbers, and they cannot be adjacent in this case. Therefore, the sum of the two other small numbers (besides 1 and 2) is no more than 10. And the sum of the small numbers is no more than 13. Example: $8,6,7,1,3$, $2,5,4$.

Criteria. Only the correct answer and example: 2 points.