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TOT 406 1994 Spring A J4 numbers in 10x10

Source:

June 12, 2024
combinatorics

Problem Statement

Prove that among any 1010 entries of the table 0    1    2    3    ...    90 \,\,\,\, 1 \,\,\,\, 2 \,\,\,\, 3 \,\,\,\, ... \,\,\,\, 9 9    0    1    2    ...    89 \,\,\,\, 0 \,\,\,\, 1 \,\,\,\, 2 \,\,\,\, ... \,\,\,\, 8 8    9    0    1    ...    78 \,\,\,\, 9 \,\,\,\, 0 \,\,\,\, 1 \,\,\,\, ... \,\,\,\, 7 1    2    3    4    ...    01 \,\,\,\, 2 \,\,\,\, 3 \,\,\,\, 4 \,\,\,\, ... \,\,\,\, 0 standing in different rows and different columns, at least two are equal.
(A Savin)
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