Puzzle ZNOJ - BrainBashers

Trade Convention #1all logic puzzles

Workers with the surnames Baker, Teacher, Carpenter, and Plumber are currently attending an annual convention.

No-one is currently, nor has ever been, in the same occupation as their name, and no-one has had the same occupation twice.
Charlie has never been a carpenter, and Mr Teacher is now a plumber.
Davie used to be a teacher, but Mr Billie Baker never has.
Mr Plumber is not called Eddie, and Mr Carpenter wasn't previously a teacher.
The previous occupations were all different, and the current occupations are all different.
Can you determine the full names of each of the attendees, along with their current and previous occupation?

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Hint
Find out who used to be the teacher first.

Answer
Billie  Baker     –    plumber   + carpenter
Eddie   Teacher   –    carpenter + plumber
Charlie Carpenter –    baker     + teacher
Davie   Plumber   –    teacher   + baker

The previous occupation is followed by the current.

Reasoning
The four forenames are: Billie, Charlie, Davie, Eddie.
The four surnames are: Baker, Teacher, Carpenter, Plumber
The four occupations are: baker, teacher, carpenter, plumber.

By (3), we have Billie Baker:
Billie  Baker     –    ?         + ?
        Teacher   –    ?         + ?
        Carpenter –    ?         + ?
        Plumber   –    ?         + ?

By (2), Mr Teacher is currently a plumber:
Billie  Baker     –    ?         + ?
        Teacher   –    ?         + plumber
        Carpenter –    ?         + ?
        Plumber   –    ?         + ?

By (3) Mr Baker was not previously a teacher. By (4), neither was Mr Carpenter. And by (1) Mr Teacher can't have been either. Therefore, Mr Plumber used to be a teacher, and is called Davie:
Billie  Baker     –    ?         + ?
        Teacher   –    ?         + plumber
        Carpenter –    ?         + ?
Davie   Plumber   –    teacher   + ?

By (3), Mr Baker has never been a teacher, and by (1), Mr Plumber can't currently be a teacher either. Also, by (1), neither can Mr Teacher. Therefore, Mr Carpenter must currently be a teacher:
Billie  Baker     –    ?         + ?
        Teacher   –    ?         + plumber
        Carpenter –    ?         + teacher
Davie   Plumber   –    teacher   + ?

By (1), Mr Baker can't be a baker, so only Mr Plumber can currently be a baker. Leaving Mr Baker as a carpenter currently:
Billie  Baker     –    ?         + carpenter
        Teacher   –    ?         + plumber
        Carpenter –    ?         + teacher
Davie   Plumber   –    teacher   + baker

By (1), only Mr Teacher could have previously been a carpenter:
Billie  Baker     –    ?         + carpenter
        Teacher   –    carpenter + plumber
        Carpenter –    ?         + teacher
Davie   Plumber   –    teacher   + baker

By (2), Charlie has never been a carpenter, and since Mr Teacher has, Charlie must be Mr Carpenter.
Billie  Baker     –    ?         + carpenter
        Teacher   –    carpenter + plumber
Charlie Carpenter –    ?         + teacher
Davie   Plumber   –    teacher   + baker

By (1), we now know all of the occupations, and Eddie must be Mr Teacher:
Billie  Baker     –    plumber   + carpenter
Eddie   Teacher   –    carpenter + plumber
Charlie Carpenter –    baker     + teacher
Davie   Plumber   –    teacher   + baker