To demonstrate set union and intersection to her class, Mrs. Putnam asked for three students to each write down a set of numbers.

After they had done so, she looked at their sets and told the class, "the union of these three sets is the first ten counting numbers, but their intersection is empty!"

How many triples (A, B, C) of sets are there such that

A U B U C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
and
A ∩ B ∩ C = {} ?

(In reply to re(2): my solution by Ady TZIDON)

I did allow one empty set: they count among the 3^10, and in tracking unordered triples, I added 3, rather than subtracting 3, before the division by 6. Those are precisely the double null-set triples that are counting.

But this is moot, as SK has pointed out, and as Brian Smith has incorporated in his solution: a given number (given element) may appear in two of the sets.

Posted by Charlie on 2004-02-10 11:07:22