MathDB

10.2

Part of 2021 Kyiv City MO Round 1

Problems(1)

Almost magic square with a twist

Source: Kyiv City MO 2021 Round 1, Problem 10.2

12/21/2023
The 1×11 \times 1 cells located around the perimeter of a 4×44 \times 4 square are filled with the numbers 1,2,…,121, 2, \ldots, 12 so that the sums along each of the four sides are equal. In the upper left corner cell is the number 11, in the upper right - the number 55, and in the lower right - the number 1111.
https://i.ibb.co/PM0ry1D/Kyiv-City-MO-2021-Round-1-10-2.png
Under these conditions, what number can be located in the last corner cell?
Proposed by Mariia Rozhkova
permutationsconstructioncombinatorics