9.4. Natural numbers from 1 to 100 are written on cards, one number per card. Vasya forms sets of three cards such that in each set, one of the numbers equals the product of the other two. What is the maximum number of such sets Vasya could have formed? (The same card cannot be used in two sets.)
Answer: 8 sets.

## Solution.

Estimation. It is obvious that each set must contain at least one single-digit number, since the product of two different two-digit numbers is greater than 100. The number 1 cannot be included in any set, as all our numbers are distinct. Therefore, no more than 8 sets can be formed.

Example. 8 sets can be formed. For example, (9, 11, 99), (8, 12, 96), (7, 13, 91), (6, 14, 84), (5, 15, 75), (4, 16, 64), (3, 17, 51), (2, 18, 36).

## Criteria.

7 points. Correct solution with the correct answer.

3 points. There is an estimation that there are no more than 8 sets, but no example is provided.

3 points. There is an example of 8 sets, but no estimation is provided.

0 points. Only the correct answer.