Here's a problem by puzzle composer Hubert Phillips called “Pickled Walnuts”. What conclusions (if any) can be drawn about armadillos and picked walnuts, assuming all statements are true?
- Pickled walnuts are always provided at Professor Piltdown’s parties.
- No animal that does not prefer Beethoven to Mozart ever takes a taxi in Bond Street.
- All armadillos can speak the Basque dialect.
- No animal can be registered as a philatelist who does not carry a collapsible umbrella.
- Any animal that can speak Basque is eligible for the Tintinnabulum Club.
- Only animals that are registered philatelists are invited to Professor Piltdown’s parties.
- All animals eligible for the Tintinnabulum Club prefer Mozart to Beethoven.
- The only animals that enjoy pickled walnuts are those who get them at Professor Piltdown’s. (You can assume he's referring to Professor Piltdown's parties.)
- Only animals that take taxis in Bond Street carry collapsible umbrellas.