Brain Teasers
Turners and Lerners
Quinn, Ralph, and Steve each belong either to the Turner family, who always tells the truth, or the Lerner family, who always lies. Quinn says, "Either I belong or Ralph belongs to a different family than the other two." Whose family can be determined?
Answer
We know Ralph's family, and he is a Lerner.If Quinn is telling the truth, then he is from the Turner family. Then he is either the only member of the Turner family, or Ralph belongs to a different family than the other two, making Ralph the only Lerner. If Quinn is lying, then he is from the Lerner family. Then either Steve belongs to a different family than the other two, making him the only Turner, or all three are Lerners.
In all four situations, Ralph is a Lerner.
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Comments
Elegant. I like puzzles where there does not seem to be enough information to solve it. I like puzzles where you don't get to a single definitive solution, but multiple solutions with something in common. This has both. interesting enough to require some thought; easy enough to do in your head. Very nice.
This was a rather easy one. After solving it with pencil and paper I wrote a tiny scip model to let the machine find the solution. The model can be found at https://gist.github.com/
fcdec88ab8a4b8ea30937918cbba7ed4
fcdec88ab8a4b8ea30937918cbba7ed4
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