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 my solution by Ady TZIDON)

Are you saying ({1,2,3,4},{5,6,7,8,9,10},{}), for example, shouldn't be counted as one of the triplets?

Posted by Charlie on 2004-02-10 10:52:08