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

solution by Charlie)

Charlie (and others working on this),

Am I misreading the problem when I suggest that the triples might be something like:

{1, 2, 3, 4, 5, 6}

{4, 5, 6, 7, 8}

{8, 9, 10}

... where 4, 5, 6, and 8 are all in more than one set?

The conditions of the problem (the union and intersection) still hold, but your statement "*Each of the elements belongs to [only] one of the three sets*" and your math, has the implication of the added word 'only'.

I think you need to account for this.

- SK