MathDB
2012 ToT Fall Junior A p3 even 2 x 2 sub-tables in 11x 11 table

Source:

March 22, 2020
combinatorics

Problem Statement

Some cells of a 11×1111 \times 11 table are filled with pluses. It is known that the total number of pluses in the given table and in any of its 2×22 \times 2 sub-tables is even. Prove that the total number of pluses on the main diagonal of the given table is also even. (2×22 \times 2 sub-table consists of four adjacent cells, four cells around a common vertex).