46th Putnam 1985 Problem A1 How many triples (A, B, C) are there of sets with union A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A ∩ B ∩ C = ∅ ? Solution
: 6 10 . Easy. Careful. The answer is not 3 10 (this trap is the only reason I do not rate the problem trivial!). There are six possibilities for each element: just A, just B, just C, not A (meaning B and C, but not A), not B, or not C. 46th Putnam 1985 © John Scholes jscholes@kalva.demon.co.uk 3 Nov 1999