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ne can find a rectangle $1\times k$ in which the sum of the numbers equals $0$

Source: Caucasus MO 2023

July 16, 2023

Problem Statement

Is it possible to fill a table 1×n1\times n with pairwise distinct integers such that for any k=1,2,…,nk = 1, 2,\ldots, n one can find a rectangle 1×k1\times k in which the sum of the numbers equals 00 if a) n=11n= 11; b) n=12n= 12?
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