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All the sixes

I have before me six different six-digit numbers, whose sum also contains six digits. Each of the 42 digits has one of only two values. If I told you the sum, you would be able to identify all six numbers. What is the sum?

WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 18 July. The Editor’s decision is final. Please send entries to Enigma 1702, New ÐÓ°ÉÔ­´´, Lacon House, 84 Theobald’s Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).

Answer to 1696 Leftovers: One coloured ball remained, and four red

The winner Michael Hubbard of Harlow, Essex, UK