Problem

Source: Kyiv City MO 2024 Round 1, Problem 8.2

Tags: number theory, prime numbers



Write the numbers from 1 to 16 in the cells of a of a 4×4 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 4×4 square, the sum of numbers in them is a prime number The figure below shows examples of such pairs of cells, sums of numbers in which have to be prime. Proposed by Mykhailo Shtandenko