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Filling a 6x6 table

Source: 44th International Tournament of Towns, Junior O-Level P1, Fall 2022

February 16, 2023
Tournament of Townscombinatorics

Problem Statement

Is it possible to arrange 3636 distinct numbers in the cells of a 6×66 \times 6 table, so that in each 1×51\times 5 rectangle (both vertical and horizontal) the sum of the numbers equals 20222022 or 20232023?
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