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TOT 391 1993 Autumn O S3 1-25 in 5x5 table

Source:

June 12, 2024
combinatoricsalgebra

Problem Statement

Each of the numbers 1,2,3,...251, 2, 3,... 25 is arranged in a 55 by 55 table. In each row they appear in increasing order (left to right). Find the maximal and minimal possible sum of the numbers in the third column.
(Folklore)