You are at a wedding reception in Knave City and are talking with someone (a knight, knave or liar) who makes the following statements:
Chris is married to Alice.
Either Alex is married to Coral or Bob is married to Alice but not both.
Either Alex isn't married to Betty or Chris isn't married to Coral but not both.
I am a knight.
The maid of honor (who is a knight) tells you whether the third statement is true or false. From that, you could figure out who is married to whom...
There are only 6 possible sets of pairings. Here they are with the resulting truth values of the statements:
Men ABC ABC ABC ABC ABC ABC
Women ABC ACB BAC BCA CAB CBA
Statement 1 F F F T F T
Statement 2 F F T F F T
Statement 3 T F F T F F
Statement 4 F F F F F F
There are two columns where you could be speaking to a liar, and one where you're speaking to a knave. But we also know that if we were truthfully told the truth or falsehood of the third statement, we'd be able to figure it out. If we were told it was false we still wouldn't be able to tell if the order of women married to ABC were ACB or CAB. But if we know (as must be the case) that the third statement was true, then the speaker is a knave and the women married to A,B,C are B,C,A respectively.
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Posted by Charlie
on 2007-04-03 11:36:17 |
solution
