P6

Part of STEMS 2024 Math Cat B

Problems(1)

prove all the rational points are colored the same

Source: STEMS 2024, CAT B, P6

All the rationals are coloured with

n

colours so that, if rationals

a

b

are colored with different colours then

\frac{a+b}2

is coloured with a colour different from both

a

b

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