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8*8 board and the numbers 1,2,3,...,64

Source: Azerbaijan 2022 Junior National Olympiad

May 14, 2022
combinatoricsJuniorAzerbaijanBound

Problem Statement

There is a 8∗88*8 board and the numbers 1,2,3,4,...,63,641,2,3,4,...,63,64. In all the unit squares of the board, these numbers are places such that only 11 numbers goes to only one unit square. Prove that there is atleast 44 2∗22*2 squares such that the sum of the numbers in 2∗22*2 is greater than 100100.
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