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?

Your mutual acquaintance has been rather helpful, he's actually given you too much information.

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

either                      BD   CE   [AF]
or (being none of     BE    CD    AF
         the above       BF    CD    AE
         couples)         BE    CF    AD

Your mutual acquaintance can't help you out by telling you one specific couple. However if he told you a couple whose above pairings are not in bold, you could instantly work out the other two.

So therefore all the couples must be in bold. Bert lived happily ever after with Elaine, Charles and Daphne are already expecting their first child, and Albert and Francine got a divorce soon afterwards and she took his house.

Posted by Amber on 2005-07-27 04:02:40