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?

(In reply to Three couples, one problem (in Logic) by Solomon)

Hi, I noticed a lot of people have posted the correct answer so I'll not bother with that.  I did see two statements you hadn't justified:

"Not possible 1:
Albert could not be married to Daphne, because then Charles would be married to Francine, leaving Bert married to Elaine"

okay so far

 "which could not happen [Bert married to Elaine] because this condition can only be satisfied if Albert is married to Francine. " Why? I can't see a reason why (Bert, Elaine) => (Albert, Francine) from the hints given...

"Not possible 2:
Bert married Daphne and Charles married Elaine is not possible because Albert could marry Francine only if Bert marrie Elaine. " Again, I can't see how this is justified (Albert, Francine) <=> (Bert, Elaine) in the text!

So you can't justify your final conclusion, which must be wrong because if the 'mutual aquaintance' tells you that Albert married Elaine, then you know that Bert married Francine, so you know that Charles married Daphne but the mutual aquaintance said that knowing one specific couple wouldn't help you!

Posted by Peter on 2005-08-01 02:42:08