Return of the caskets
Remember the Bellini and Cellini families? The ones who back in the day made caskets? The families were best of friends and would often collaborate on making a set of caskets. Bellini and his sons only put true inscriptions on the ones they made, and Cellini and his sons only put false inscriptions on the ones they made.
I recently encountered a set of caskets inscribed as follows:
Casket A: At least one of these caskets was made by one of the sons.
Casket B: At most one of these caskets was made by a member of the Bellini family.
Who made each casket?
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1 solution
Consider the statement on casket B. If it is false, then both caskets were made by members of the Bellini family. But then you'd have a Bellini-inscribed casket with a false statement, which is a contradiction. So the statement on casket B must be true, which means it was made by a member of the Bellini family. Thus, B must be the "at most one" casket made by a member of the Bellini family, so A was made by a member of the Cellini family.
Therefore, the statement on casket A is false. Neither casket was made by one of the sons, so since the statement on A is false and the one on B is true, A was made by Cellini himself and B was made by Bellini himself.