Problem 1. Petya has a $3 \times$ 3 table. He places chips in its cells according to the following rules:

- no more than one chip can be placed in each cell;
- a chip can be placed in an empty cell if the corresponding row and column already contain an even number of chips (0 is considered an even number).

What is the maximum number of chips Petya can place?
Solution. Answer: 9.

Let $a, b, c$ denote the left, middle, and right columns of the table, and $1, 2, 3$ denote the bottom, middle, and top rows of the table. Petya can fill all 9 cells of the table with chips, for example, in the following order: $a 1, b 2, c 3, a 2, b 3, c 1, a 3, b 1, c 2$. Obviously, it is not possible to place more than 9 chips.

## Criteria

The largest suitable criterion is used:

7 6. Any complete solution to the problem.

2 p. There is only the correct answer (the algorithm for placing the chips is missing).