All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Set Me Up (Posted on 2004-02-10) Difficulty: 3 of 5
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 = {} ?

See The Solution Submitted by DJ    
Rating: 4.3636 (11 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution | Comment 8 of 31 |
(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
  Posted by SilverKnight on 2004-02-10 10:56:23

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information