Three friends of mine (Albert, Bert and Charles) married three girls (Daphne, Elaine and Francine) but I didn't know who married whom. I asked a mutual acquaintance about the marriages, and he said:

"Well, work it out. If Albert married Elaine, then Bert married Francine, and vice versa."

I said, "That's not enough; can you give me other hint?"

"Right. Either Bert married Daphne and Charles married Elaine, or neither of these couples happened."

"Still not enough, give me something else."

"Let's see... Charles married Francine if and only if Albert married Daphne."

"You are still not helping. Couldn't you tell me at least one specific couple, any one, so I can work out the other two myself?"

He smiled. "That wouldn't help you."

I thought a little, and I knew the three pairs. Who married whom?

Here's the pairings that would lead to a solution

AE->BF->CD

AD->CF->BE

BF->AE->CD

BD->CE->AF

CE->BD->AF

CF->AD->BE

Leaving the following pairings as the only ones that "wouldn't help"

AF which implies only !BF and !CF, from the rules stated in the game or indeed, from the rules of marriage itself.

BE which only leads you to the logical conclusion of !AE and !CE. 

CD which implies only !AD and !BD.

Solution (AF, BE, CD)

Posted by Bob Smith on 2005-07-25 14:56:22