7.5. The numbers from 1 to 20 are arranged in a circle. We will paint a number blue if it is divisible without a remainder by the number to its left. Otherwise, we will paint it red. What is the maximum number of blue numbers that could be in the circle?
# Solution.

Evaluation. It is obvious that numbers cannot be blue if the number to their left is greater than or equal to 11. That is, no more than 10 numbers can be blue.

Example. As an example, both any correct arrangement and a correct algorithm are counted. An example of a correct algorithm.

1) write down the number 20
2) if the last written number $=2 \mathrm{k}$, then write the number $\mathrm{k}$ to its left, otherwise write the largest unused number to its left.
3) while there are unused numbers - repeat step 2.

## Criteria.

7 points for having both the evaluation and a correct example

4 points for only the example

3 points for only the evaluation.