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: Solution - not yet? by SilverKnight)

In the choices for where a given number could go, there were six choices; none of them was A and B and C. Any given number went into at most two subsets. I think Brian had it right.

Posted by Charlie on 2004-02-10 13:24:41