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prove all the rational points are colored the same

Source: STEMS 2024, CAT B, P6

December 17, 2023

combinatorics

Problem Statement

All the rationals are coloured with

n

colours so that, if rationals

a

and

b

are colored with different colours then

\frac{a+b}2

is coloured with a colour different from both

a

and

b

. Prove that every rational is coloured with the same colour.