I am looking for an elegant way to solve this rather simple logic puzzle using mathematical logic (statements, conjunctions, disjunctions, implications, tautologies, predicate logic and so on). I am not looking for a solution using combinations, variations or permutations, as I have already solved it using that method (given below).
The puzzle is:
Four men (A, B, C, D) should be seated in a boat forming a line. Can you determine the order in which they need to be seated, from the front of the boat to the back, so that all of their requests are satisfied?
Requests:
Man A: I want to be seated at one end of the boat (either first or last) only if B sits next to me.
Man B: I don't want to sit next to (either before or after) C and I don't want to be last.
Man C: I don't want to sit next to A if I am seated on one end of the boat.
Man D: I want to sit next to B or not to sit next to A, and if I am not first, then I want to be last (if not seated on the front side, he wants to sit at the back side of the boat).
There obviously are $V_{4}^{4}=P_{4} = 4! = 24$ possibilities for this exercise (not sure if the notation is universal), of which only one - "BACD", satisfies the conditions. However, had there been five elements in the example, it wouldn't have been so easy to determine the correct result by experimentation/counting values, which is why I am searching for a logical approach to the problem.