Who is Gauss's wife?

[Countolaf]

Four pairs go together to a club. Their names are Cintia, Teresa, Aguida, Gladys, Newton, Arquimedes, Pitagoras and Gauss. (Cintia, Teresa, Aguida and Gladys are women and Newton, Arquimedes, Pitagoras and Gauss are men) In a certain moment:
1. Newton's wife doesn't dance with her husband. She dances with Cintia's husband.
2. Arquimedes plays guitar and Aguida plays piano.
3. Gladys and Gauss don't dance.
4. Gladys isn't Arquimedes's wife.
5. Who is Gauss's wife?

[Fox Mc Cloud]

Arquimedes and Aguida are together, means 6 ppl left. I think one of the names in 1, 2.. or 5 is wrong.

[Countolaf]

Everything is correct, Fox.

[Fox Mc Cloud]

I would say Gladys.

[Countolaf]

How did you guess, Fox?

[Fox Mc Cloud]

Because they both don't dance but can you explain how it actually works?

[Countolaf]

We will use O for married with, X for not married with, and - for unknown.
1) We make a table:

	Newton	Arquimedes	Pitagoras	Gauss
Cintia	-	-	-	-
Teresa	-	-	-	-
Aguida	-	-	-	-
Gladys	-	-	-	-

2) Using affirmation 4:

	Newton	Arquimedes	Pitagoras	Gauss
Cintia	-	-	-	-
Teresa	-	-	-	-
Aguida	-	-	-	-
Gladys	-	X	-	-

3) Using affirmation 1:

	Newton	Arquimedes	Pitagoras	Gauss
Cintia	X	-	-	-
Teresa	-	-	-	-
Aguida	-	-	-	-
Gladys	-	X	-	-

4) Using affirmations 1 and 3:

	Newton	Arquimedes	Pitagoras	Gauss
Cintia	X	-	-	X
Teresa	-	-	-	-
Aguida	-	-	-	-
Gladys	X	X	-	-

5) Using affirmations 1 and 2:

	Newton	Arquimedes	Pitagoras	Gauss
Cintia	X	X	-	X
Teresa	-	-	-	-
Aguida	X	-	-	-
Gladys	X	X	-	-

6) Then we get:

	Newton	Arquimedes	Pitagoras	Gauss
Cintia	X	X	O	X
Teresa	O	-	-	-
Aguida	X	-	-	-
Gladys	X	X	-	-

7) Now:

	Newton	Arquimedes	Pitagoras	Gauss
Cintia	X	X	O	X
Teresa	O	X	X	X
Aguida	X	-	X	-
Gladys	X	X	X	-

8) Finally:

	Newton	Arquimedes	Pitagoras	Gauss
Cintia	X	X	O	X
Teresa	O	X	X	X
Aguida	X	O	X	X
Gladys	X	X	X	O

From the table, Gladys is Gauss's wife.
You can find faster than this, but I wanted to show all the pairs.

[Fox Mc Cloud]

Nice explanation .