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Important

The variants of this puzzle do not have any relation to each other. For example, just because Alice and Bob must cover mathematics and physics in easy mode doesn't mean that Charlie must be an engineer in the original problem.

Easy mode

You are only with Alice and Bob at Boolos' Brewery, and the only fields of expertise present (besides yours) are mathematics and physics. Otherwise, the situation is the same as the main version.

How many questions do you need to determine Alice's and Bob's respective fields of expertise?

Note

This reduces to a different classic logic puzzle, and you can determine both fields of expertise with only one question.

The "Hardest"-er Logic Puzzle Ever ™️

You are at Boolos' Brewery with Alice, Bob, Charlie, and Dan. Among them, the fields of expertise are mathematics, physics, engineering, and philosophy.

Since you study computer science, they decide it would be "fun and quirky" to only respond to your yes/no questions with foo, bar, or baz. There are three responses thanks to the philosopher: they insisted that yes/no questions have at least three possible responses. (It had something to do with excluding the middle, but everyone considered excluding the philosopher after that, especially you once you figure out who the philosopher is.)

  1. The mathematician uses classical foundations, and decided on a convention for which of the three words corresponds to "yes", and which of the other two words corresponds to "no". In particular, the mathematician never uses the remaining word.
  2. The physicist, while more into "quantum supersymmetry" than anything classical, also excludes the middle. They use the same words as the mathematician, but with opposite convention: the mathematician's word for "yes" is the physicist's word for "no", and vice versa.
  3. You'd think the philosopher would use all three words, but "how can one truly know anything?" The philosopher therefore answers every yes/no question with the only word not being used by the mathematician (or the physicist).
  4. The engineer didn't pay attention when conventions were made, but is trying to fit in, so they respond to any yes/no question with a random choice of foo, bar, or baz.

How many questions do you need to determine everyone's respective fields of expertise?

Note

I can determine everyone's respective fields in at most seven questions. Can you do better?