Three people at a party: Alex is married, we don't know much about Betty and Chris is unmarried.
We notice that Alex is constantly staring at Betty, but Betty is only looking at Chris all the time.
This seems to be yet another case of a married person looking for too long at an unmarried person.
But can we be sure? What is the probability that this ABC conjecture is true?
7 comments:
I don't know where to start on this one. But Betty could be the wife of Alex and Chris could be their son or daughter.
No "could" ... just the question: Is a married person staring at an unmarried person ? Or do we not have enough information to answer that?
0.5?
Alright, here is how to prove this ABC conjecture:
There are only two possibilities: Either Betty is married or she is unmarried.
In the first case a married person (Betty) is looking at an unmarried person (Chris).
In the other case a married person (Alex) is looking at an unmarried person (Betty).
Tertium non datur.
Btw we use this as a question in job interviews and it is interesting how many people have a problem with it ...
More to the point, why are you inviting these people to your party? Constantly staring is beyond rude and definitely creepy.
Ha - but I'm actually not a great fan of parties, political or otherwise ...
I guess the point of my little joke, if it had one, was that people have a lot of wetware devoted to analyzing relations among humans, so our most natural instinct when confronted with a problem stated in human terms is to analyze it in terms of human relations, like Lee did. That's what's going on in some of the puzzles of Kahneman and Tversky, and why your puzzle is hard. I think that if it was stated in purely logical terms, without the fraught human relations implications, it would be an easier puzzle.
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