# UKMT Special (Problem $6$)

Ten balls, each coloured green, red or blue, are placed in a bag.

Ten more balls, each coloured green, red or blue, are placed in a second bag.

In one of the bags there are at least seven blue balls and in the other bag there are at least four red balls.

Overall there are half as many green balls as there are blue balls.

Prove that the total number of red balls in both bags is equal to either the total number of blue balls in both bags or the total number of green balls in both bags.

[UKMT Cayley Olympiad $2015$, Q$4$]

Note by Yajat Shamji
8 months, 2 weeks ago

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