Mij the magician has a large bag of red balls and a large bag of green balls. Mij wanders round the audience selecting volunteers, asking each volunteer to remove two balls, one from each bag, until of the red balls and of the green balls have been removed. The balls remaining in the bags are then emptied into a bucket.
What fraction of all the balls does the bucket contain?
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Cayley Mathematical Olympiad 2006 (2006)
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