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integers in fields of a 19 x 19 table

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1993 p2

February 20, 2020
combinatorics

Problem Statement

In fields of a 19×1919 \times 19 table are written integers so that any two lying on neighboring fields differ at most by 22 (two fields are neighboring if they share a side). Find the greatest possible number of mutually different integers in such a table.