Rearrange numbers such a sum in all 1 \times 3 rectangles doesn't change
Source: Saint Petersburg olympiad 2024, 11.1
September 22, 2024
combinatoricsalgebra
Problem Statement
The table is filled with numbers from to as shown in the figure. Is it possible to rearrange some numbers so that there is still one number in each cell, and so that the sum of the numbers does not change in all rectangles of three cells?