coloring n numbered cards from 1 to n with 3 colors
Source: Polish Math Olympiad 2021 2nd round p1 day 1
May 31, 2021
combinatoricsColoring
Problem Statement
Jacek has cards numbered consecutively with the numbers , 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 , then the card number , 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.