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 $4$ ]

#Combinatorics

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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Comments

You have until this Sunday, $3:00$ pm!

Yajat Shamji - 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

UKMT Special (Problem 666)

Comments

UKMT Special (Problem $6$ )