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?
There are six possible pairings: AD+BE+CF, AD+BF+CE, AE+BD+CF,
AE+BF+CD, AF+BD+CE, and AF+BE+CD
.All three statements are equivalent to
saying that the second and third cases are valid, so we are left with
four possibilities: AD+BE+CF, AE+BF+CD, AF+BD+CE, and AF+BE+CD.
Out of
the nine possible man/woman pairs, six appear only once, so if my friend had
named one of those, I would have known the other two pairs.
The other
three pairs are AF, BE, and CD, which appear twice -- but only once
together, without any of the other six pairs.
Edited on July 26, 2005, 6:09 pm
Reasoned out
