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writing numbers in 5x120 board (Ukraine 1998 Grade 8 P6)

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June 4, 2021
combinatorics

Problem Statement

Show that it is possible to write a number from the set {1,2,3,4,5}\{1,2,3,4,5\} in each square of a 5×1205\times120 board (55 columns and 120120 rows) so that the following conditions are satisfied:
(i) all numbers in the same row are distinct; (ii) all rows are distinct; (iii) the board can be partitioned into 2424 5×55\times5 boards which can be reassembled (without rotating and turning over) into a 120×5120\times5 board whose 120120 columns are distinct.
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