2. A notebook costs 10 rubles. Eight children bought notebooks, and each had a different non-zero amount of rubles left, but none had enough for another notebook. The children pooled their remaining rubles, and it was exactly enough to buy several more notebooks. How much money did each child have left before pooling?
Answer: $1,2,3,4,6,7,8,9$.

Solution. Let's take all possible non-zero remainders when dividing by $10: 1,2, \ldots, 9$. The sum of all 9 remainders is 45. We need to exclude one remainder so that the sum of the remaining ones is divisible by 10. Clearly, there is only one possibility: to exclude the remainder 5.

Comment. Correct solution - 20 points. There is a gap in the justification - 15 points. The solution is started, there is some progress - 5 points. The solution is started, but there is no noticeable progress - 1 point. The correct answer is given without explanations - 0 points.