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The same chance

Harry and Tom each had a set of 15 red and six coloured snooker balls. Each of them had a bag, into which he put one or more of the red balls and four or more of the coloured balls from his set. Although Tom put more balls into his bag than Harry put into his bag, each of them calculated that if he picked four balls out of his bag simultaneously at random there was a 1 in X chance that all four would be coloured.

X represents the same number for each of them. What number?

WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 29 July. The Editor’s decision is final. Please send entries to Enigma 1551, ¿ìè¶ÌÊÓƵ, Lacon House, 84 Theobald’s Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).

Answer to 1545 Dressed up to the nines: The numbers were 413, 568 and 927

The winner Johan Uys of Bellville, South Africa