46th Putnam 1985

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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

Answer: 610.

Easy.

Careful. The answer is not 310 (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