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naturals in 13x13 grid, sum of numbers at 8 squares divisible by 8

Source: 2017 Latvia BW TST P6

December 18, 2022
combinatoricsdivisiblenumber theory

Problem Statement

A natural number is written in each box of the 13×1313 \times 13 grid area. Prove that you can choose 22 rows and 44 columns such that the sum of the numbers written at their 88 intersections is divisible by 88.
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