1. Vasya thought of a four-digit number and for each pair of its adjacent digits, he wrote down their product on the board. After that, he erased one product, and the numbers 20 and 21 remained on the board. What is the smallest number Vasya could have thought of?
Answer: 3745.

Solution. Since the products 20 and 21 are given, the digits of the thought-of number include 4, 5 and 3, 7, meaning we know all its digits. The digits 4 and 5, 3 and 7 must be adjacent, so the smallest number that meets the conditions is 3745, and Vasya erased the product $7 \cdot 4=28$.

Criteria. Only the answer - 3 points. Noted that the digits 4 and 5, 3 and 7 are adjacent - another 4 points. Full solution - 7 points.