Mr A, Miss B, Mr C and Miss D are sitting around a table and each one has a different trade: cook, barber, washer man and tailor. It is known that Mr A sits opposite the cook, Miss B sits to the right of the barber, the washer man sits on the left of the tailor, and Miss D sits opposite Mr C. What are the trades of A and B respectively?

Introduction / Context:
This reasoning problem combines a circular seating arrangement with assignment of different trades to four people. The question gives positional clues about who sits opposite whom and who sits to the right or left of which trade. Our goal is to use these clues to determine the trades of Mr A and Miss B specifically. The puzzle tests spatial reasoning and the ability to reconcile several relative position statements at once.

Given Data / Assumptions:

• Four people sit around a circular table: Mr A, Miss B, Mr C, Miss D.
• The four trades are cook, barber, washer man, and tailor, one for each person.
• Mr A sits opposite to the cook.
• Miss B sits to the right of the barber.
• The washer man sits on the left of the tailor.
• Miss D sits opposite Mr C.
• Right and left are considered with respect to the centre of the table in the same direction of seating order.

Concept / Approach:
To solve, we place the four seats around a circle and use opposite pairs and relative left right positions. We first fix one person in a reference position, because circular problems are rotationally symmetric. Then we place the second person opposite where required, and gradually assign trades that satisfy left and right relationships. In such small puzzles, we can test possible assignments one by one and quickly eliminate inconsistent combinations until a single valid seating and trade assignment remains. The trades of A and B can then be read from this configuration.

Step-by-Step Solution:
Step 1: Place Mr C at any seat as a reference, for example at the top. Because Miss D sits opposite Mr C, Miss D must sit directly opposite.Step 2: The remaining two seats are then occupied by Mr A and Miss B in some order. We do not yet fix which is where.Step 3: Use the condition Mr A sits opposite the cook. So whoever is cook must be seated facing Mr A, that is, the person sitting directly opposite A.Step 4: Use the condition that the washer man sits to the left of the tailor. Around the table this fixes a particular adjacency relationship between those two trades.Step 5: Apply the condition that Miss B sits to the right of the barber. So Miss B must occupy the seat immediately clockwise from whoever has the barber trade.Step 6: When all possibilities are tested consistently, the only arrangement that satisfies every condition has Mr A as the tailor and Miss B as the cook, while Mr C and Miss D take the remaining two trades.

Verification / Alternative check:
Check that in the found configuration Mr A is opposite the cook. Since Miss B is the cook and sits across from A, this condition holds.Confirm that the washer man sits on the left of the tailor. With Mr A as tailor, the washer man is placed on his left, matching the rule.Check that Miss B sits to the right of the barber and that Miss D is opposite Mr C. All statements are satisfied simultaneously, so the arrangement is valid.

Why Other Options Are Wrong:
Option A (Tailor and barber) assigns Miss B as barber, but then it is impossible for her to sit to the right of the barber because she would be the barber herself.Option C (Barber and cook) makes Mr A the barber, which conflicts with the requirement for the washer man to sit to the left of the tailor under the remaining placements.Option D (Washer man and cook) fails to satisfy the opposite relations along with the left right constraints when tested thoroughly.

Common Pitfalls:
A common mistake is to forget that in a circle there are two possible directions for right and left, so students sometimes mirror the positions incorrectly.Another pitfall is to stop checking after a few conditions seem to fit, without verifying that all given statements hold simultaneously.

Final Answer:
The only consistent assignment is that Mr A is the tailor and Miss B is the cook, so the correct answer is Tailor and cook.