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5x5 arrays defined in function of 2x2 subarrays

Source: BMO 2019, Shortlist

October 1, 2019
linear algebramatrixBalkannumber theory

Problem Statement

Determine the largest natural number N N having the following property: every 5×5 5\times 5 array consisting of pairwise distinct natural numbers from 1 1 to 25 25 contains a 2×2 2\times 2 subarray of numbers whose sum is, at least, N. N.
Demetres Christofides and Silouan Brazitikos
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