Kuzneuvv A.

A square box of candies is divided into 49 equal square cells. In each cell lies a chocolate candy - either black or white. In one sitting, Sasha can eat two candies if they are of the same color and lie in adjacent cells, either by side or by corner. What is the maximum number of candies that Sasha can definitely eat, regardless of how the candies are arranged in the box?

#
Evaluation. For the layout shown in the left image, none of the 16 black candies can be eaten, and out of the 33 white candies, no more than 32 can be eaten due to parity.
![](https://cdn.mathpix.com/cropped/2024_05_06_39c3940b0a0b7bafc849g-02.jpg?height=280&width=802&top_left_y=1269&top_left_x=639)

Algorithm. We will show that 32 candies can be eaten in any layout. In a three-cell corner, a pair of candies can always be eaten. Therefore, in a $2 \times 3$ rectangle, 4 candies can be eaten. In a $7 \times 7$ square, 8 such rectangles can be placed (see the right image).

## Answer

32 candies.