Is it possible to fill a table $1\times n$ with pairwise distinct integers such that for any $k = 1, 2,\ldots, n$ one can find a rectangle $1\times k$ in which the sum of the numbers equals $0$ if a) $n= 11$; b) $n= 12$?
Source: Caucasus MO 2023
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Is it possible to fill a table $1\times n$ with pairwise distinct integers such that for any $k = 1, 2,\ldots, n$ one can find a rectangle $1\times k$ in which the sum of the numbers equals $0$ if a) $n= 11$; b) $n= 12$?