MathDB

Is it possible to write the numbers from

1

100

in the cells of a of a

10 \times 10

square so that: 1. Each cell contains exactly one number; 2. Each number is written exactly once; 3. For any two cells that are symmetrical with respect to any of the perpendicular bisectors of sides of the original

10 \times 10

square, the numbers in them must have the same parity.
The figure below shows examples of such pairs of cells, in which the numbers must have the same parity.
https://i.ibb.co/b3P8t36/Kyiv-MO-2024-7-2.png
Proposed by Mykhailo Shtandenko

Problem Statement