Brain Teasers
Heather's Fiance
Heather is engaged to either Al, Ben, Carl or Dan. Each of the four men, plus Heather, either always tells the truth or always lies. Al says, "Exactly one of us four men always tells the truth." Ben says, "Exactly one of us four men always lies." Carl says, "Heather's fiance is either Al or Ben." Heather says, "My fiance and I either always tell the truth or always lie." Who is Heather's fiance?
Answer
Ben is Heather's fiance.If Heather is telling the truth, then her fiance is a truthteller, but if she is lying, her fiance is a truthteller just the same. Now we know that Heather's fiance is a truthteller.
Suppose Carl is lying. Then Carl is not Heather's fiance, and neither is Al or Ben. This leaves only Dan, making him a truthteller. If Al is telling the truth, then he and Dan are both truthtellers, making Al a liar. So Al must be a liar, and since he and Carl are both liars, Ben must also be lying, but now, since Dan is the only truthteller, Al must be telling the truth.
This means that Carl is a truthteller, and Heather's fiance is either Al or Ben. If Al is a truthteller, then he and Carl are both truthtellers, making Al a liar. So Al must be a liar, and therefore cannot be Heather's fiance, leaving only Ben.
Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments hidden to avoid spoilers.
Follow Braingle!