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Part of 2000 Swedish Mathematical Competition

Problems(1)

each of the numbers 1, 2, ... , 10 is colored red or blue.

Source: 2000 Swedish Mathematical Competition p1

3/21/2021
Each of the numbers 1,2,...,101, 2, ... , 10 is colored red or blue. 55 is red and at least one number is blue. If m,nm, n are different colors and m+n≤10m+n \le 10, then m+nm+n is blue. If m,nm, n are different colors and mn≤10mn \le 10, then mnmn is red. Find all the colors.
combinatoricsColoring