On the board, two-digit numbers are written. Each number is composite, but any two numbers are coprime.

What is the maximum number of numbers that can be written?
Evaluation. Since any two written numbers are coprime, each of the prime numbers 2, 3, 5, and 7 can appear in the factorization of no more than one of them. If there are five or more numbers on the board, then all prime factors in the factorization of one of them must be at least 11. But this is a composite number, so it must be at least 121. This contradicts the condition. Therefore, there are no more than four numbers on the board.

Example. 25, 26, 33, 49.

## Answer

4 numbers.