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1

Part of 2021 Poland - Second Round

Problems(1)

coloring n numbered cards from 1 to n with 3 colors

Source: Polish Math Olympiad 2021 2nd round p1 day 1

5/31/2021
Jacek has nn cards numbered consecutively with the numbers 1,...,n1,. . . , n, which he places in a row on the table, in any order he chooses. Jacek will remove cards from the table in the sequence consistent with the numbering of cards: first they will remove the card number 11, then the card number 22, and so on. Before Jacek starts taking the cards, Pie will color each one of cards in red, blue or yellow. Prove that Pie can color the cards in such a way that when Jacek takes them off, it will be fulfilled at every moment the following condition: between any two cards of the same suit there is at least one card of a different color.
combinatoricsColoring