Mr. A, Miss B, Mr. C and Miss D are sitting around a circular table,…

Concept

In a circular seating puzzle with an even number of people, an “opposite” clue pairs two people up directly, because each seat has exactly one seat facing it across the table. A “right of / left of” clue instead describes an adjacent-seat relationship from the point of view of a person facing the centre of the table: for such a person, the right-hand neighbour is the one reached by moving anticlockwise around the table (as viewed from above), and the left-hand neighbour is the one reached by moving clockwise. The standard way to solve such a puzzle is to fix every opposite pair first, then walk the right/left clues around the seats that remain.

Application

1. Four people sit at the four seats of the round table, so there are exactly two opposite pairs. Miss D sits opposite Mr. C, so the only people left, Mr. A and Miss B, must be the other opposite pair.

2. Mr. A sits opposite the cook. Since Mr. A's opposite seat is Miss B's seat, Miss B is the cook.

3. Label the seats North, East, South, West going around the table, with Mr. A at North and Miss B (his opposite) at South. Mr. C and Miss D take East and West between them, in either order — either way, they remain opposite each other, so their clue is already satisfied.

4. Miss B sits to the right of the barber, i.e. Miss B is the barber's right-hand neighbour. For a person facing the centre, the seat whose right-hand neighbour is South is the West seat, so the barber occupies the West seat (whichever of Mr. C / Miss D sits there).

5. The washer man sits on the left of the tailor. The only seats not yet fixed are North (Mr. A) and East. Testing North as the tailor's seat: the seat on North's own left is East, so the washer man's seat comes out at East — consistent. Testing East as the tailor's seat instead would put the washer man at South, but South is already the cook, which is impossible. So Mr. A (North) is the tailor, and the East seat holds the washer man.

6. Mr. A is therefore the tailor and Miss B is the cook; Mr. C and Miss D hold the barber and washer man trades between them, in whichever order matches the East/West seat chosen in step 3.

Cross-check

Fixing the seats and trades as above and checking each of the four original clues against it:

• Mr. A (North) sits opposite the cook (South, Miss B) — holds.

• Miss B (South) is the right-hand neighbour of the barber (West) — holds.

• The washer man (East) sits on the left of the tailor (North) — holds.

• Miss D sits opposite Mr. C (East and West are opposite seats) — holds.

All four clues are satisfied by this seat-and-trade mapping. Mr. C and Miss D could swap the East and West seats without breaking any clue, but that swap only exchanges the barber and washer man trades between the two of them — it never changes Mr. A's or Miss B's trade. So the trades of A and B are uniquely Tailor and Cook.