perplexus.info :: Numbers : Set Me Up

Set Me Up (Posted on 2004-02-10)

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 = {} ?

Submitted by DJ

Rating: 4.3636 (11 votes)

Solution: (Hide)

6¹⁰
There are six possibilities for which set(s) each element (1-10): just A, just B, just C, not A (meaning B and C, but not A), not B, or not C.
The first answer many people arrive at is 3¹⁰, thinking that each number can belong to just one of the students, but each could also end up in two of the sets (as long as it's not in all three, it won't be in the intersection).
While one (or two) of the students would probably not be expected to have specified the null set, nothing in the problem precludes that possibility.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Is this right ?	Penny	2004-02-10 16:47:23
re(5): Solution FINAL WORD revisited	Ady TZIDON	2004-02-10 16:38:55
re(5): Solution FINAL WORD(by Charlie	Charlie	2004-02-10 15:58:42
re(4): Solution FINAL WORD(by Charlie	Charlie	2004-02-10 15:53:24
re(4): Solution FINAL WORD	Brian Smith	2004-02-10 15:13:44
re(3): Solution FINAL WORD(by Charlie	Ady TZIDON	2004-02-10 14:50:41
re(2): Solution FINAL WORD	Charlie	2004-02-10 13:30:02
re(2): Solution - not yet?	Charlie	2004-02-10 13:24:41
Is this right ?	Penny	2004-02-10 13:02:43
re: Solution FINAL WORD	Ady TZIDON	2004-02-10 13:01:06
re(3): Game, set and match !!!!	SilverKnight	2004-02-10 12:14:34
re(2): Game, set and match !!!!	Penny	2004-02-10 12:08:54
re: Game, set and match !!!!	SilverKnight	2004-02-10 11:39:29
Game, set and match !!!!	Penny	2004-02-10 11:31:50
re: Solution - not yet?	SilverKnight	2004-02-10 11:26:26
re(3): solution	SilverKnight	2004-02-10 11:13:33
re(4): my solution	Ady TZIDON	2004-02-10 11:12:54
re: Solution - I'll drink to that	Ady TZIDON	2004-02-10 11:10:41
re(3): my solution	Charlie	2004-02-10 11:07:22
re(2): solution	Charlie	2004-02-10 11:00:46
re(2): solution	Ady TZIDON	2004-02-10 11:00:42
re(2): my solution	Ady TZIDON	2004-02-10 10:58:51
Solution	Brian Smith	2004-02-10 10:58:38
re: solution	SilverKnight	2004-02-10 10:56:23
re: solution	Ady TZIDON	2004-02-10 10:55:19
re: solution	Penny	2004-02-10 10:52:13
re: my solution	Charlie	2004-02-10 10:52:08
Penny u r overlooking something again :-(	Ady TZIDON	2004-02-10 10:47:56
solution	Charlie	2004-02-10 10:45:08
my solution	Ady TZIDON	2004-02-10 10:33:08
Solution, unless I am overlooking something again :-(	Penny	2004-02-10 10:20:37

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