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 smallest possible sum of the large numbers?
Answer: 23.

Instructions. Adjacent numbers cannot be of the same type, so larger and smaller 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. 3 and 4 cannot both be large, as there are only two larger numbers, and they cannot be adjacent in this case. Therefore, the sum of the two other large numbers (besides 7 and 8) is at least 8. And the sum of the large numbers is at least 23. Example: $8,6,7,1,3,2,5,4$.

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