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