11.1 In a competition of meaningless activity, a participant recorded 2022 numbers in a circle such that each number is equal to the product of its two neighbors. What is the maximum number of different numbers that could have been used?
Solution: If there is a zero among the numbers, then its neighbors are also zeros, so all the recorded numbers will be equal to zero. We will assume that there are no zeros among the numbers. Let $a$ and $b$ be two adjacent numbers. Then on the other side of $a$ stands $a / b$, and on the other side of $b$ stands $b / a$. In other words, two numbers at a distance of 3 are reciprocals of each other, and then numbers at a distance of 6 are equal, so there are no more than $2022 / 6 = 337$ different numbers. An example can be constructed from repeating cycles of six numbers: $2, 6, 3, 1/2, 1/6, 1/3$.

## Criteria:

- Only the answer with an example without proving the maximum - 1 point.