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.
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Comments
Heather says, "My fiance and I either always tell the truth or always lie."
That can mean she always tells the truth and her fiance always lies. They are both either always telling the truth or lying. So the answer is incorrect saying that her finance must be a truthteller.
I got an answer that Carl is the fiance. Al tells the truth and the rest lie. Read it with that answer, it all aligns.
That can mean she always tells the truth and her fiance always lies. They are both either always telling the truth or lying. So the answer is incorrect saying that her finance must be a truthteller.
I got an answer that Carl is the fiance. Al tells the truth and the rest lie. Read it with that answer, it all aligns.
This was erroneous. Heather was supposed to say "My fiance and I either BOTH always tell the truth or BOTH always lie."
Since it was previously stated that all five people always lie or always tell the truth, I think we could interpret Heather's comment properly. Otherwise, she would not have added any info at all. However, the version WimpyKid proposed would remove possible confusion.
I started assuming Al told the truth, leading to a contradiction when Heather and Dan/Carl both lie. So Al is lying. I then assumed Ben is telling the truth, and that works with him as the finance. Plus, I like a world where 80% of the people tell the truth.
This was a wonderful logic puzzle. Fun to ponder and easy enough to do in your head. Perfect for a brain teaser.
I started assuming Al told the truth, leading to a contradiction when Heather and Dan/Carl both lie. So Al is lying. I then assumed Ben is telling the truth, and that works with him as the finance. Plus, I like a world where 80% of the people tell the truth.
This was a wonderful logic puzzle. Fun to ponder and easy enough to do in your head. Perfect for a brain teaser.
After rewriting the problem as a set of relations of binary variables, I used 'scip' to solve it. For anyone interested, the model that I used can be found at https://pastebin.com/8prKiiBK
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