Solving the Circular Seating Arrangement Puzzle for 6 Persons

This problem involves arranging six persons (S, O, K, U, T, and A) around a circular table, all facing the centre. We need to use the given clues to determine their exact positions and then identify the person sitting third to the left of K.

Analysing the Clues for Seating Arrangement

Let's break down the clues step-by-step to build the seating arrangement:

1. "6 persons S, O, K, U, T and A are sitting around a circular table facing towards the centre."
   There are 6 positions in the circle.
2. "Only two persons are sitting between O and A."
   In a circle of 6 people, having exactly two people between two individuals means they are sitting opposite each other. So, O and A are opposite.
3. "S is sitting second to the right of A."
   If we fix A's position, counting two positions to the right (clockwise) gives S's position.
4. "Only one person is sitting between O and U."
   From O's position, U must be in one of the two adjacent positions (one person away in either direction around the circle).
5. "T is sitting to the immediate right of K."
   K and T are sitting next to each other, with T being clockwise to K. This pair (K-T) must occupy two adjacent spots.

Determining the Seating Arrangement

Let's use the clues to place the people. Since O and A are opposite, let's represent the positions:

Suppose we number the seats 1 through 6 in a clockwise direction.

If A is at position 1, O must be at position 4 (with positions 2 and 3, or 5 and 6 between them, depending on direction; being opposite means 3 positions apart counting one arc, or 2 people between on the shorter arc). Let's assume the shorter arc rule for "between". Two people between A and O means positions are 1 and 4 in a 6-person circle.

• A is at position 1.
• O is at position 4 (opposite A).

Now use clue 2: "S is sitting second to the right of A."

• From A at position 1, the first person to the right is at position 2, and the second is at position 3.
• S is at position 3.

Current arrangement: A (1), S (3), O (4). Positions 2, 5, 6 are empty.

Now use clue 4: "Only one person is sitting between O and U."

• O is at position 4. One person between O and U means U is either at position 2 (with S at 3 between them when going anti-clockwise from O to U) or position 6 (with 5 between them when going clockwise from O to U).

Let's test the possibilities:

Possibility 1: U is at position 6.

• A (1), S (3), O (4), U (6). Remaining people are K, T for positions 2, 5.
• Clue 5: "T is sitting to the immediate right of K." This means K and T must be adjacent.
• Can K and T be placed at 2 and 5? No, they are not adjacent positions in a circle of 6 (positions 2 and 5 have 2 people between them). This possibility is incorrect.

Possibility 2: U is at position 2.

• A (1), U (2), S (3), O (4). Remaining people are K, T for positions 5, 6.
• Clue 5: "T is sitting to the immediate right of K." This means K and T must be in adjacent positions.
• Positions 5 and 6 are adjacent. If K is at 5, the immediate right (clockwise) is 6. So, T must be at 6.
• This fits: K at 5 and T at 6.

Let's check if this arrangement A(1), U(2), S(3), O(4), K(5), T(6) satisfies all clues:

• S (3) is second right of A (1)? Right of 1 is 2, then 3. Yes.
• One person between O (4) and U (2)? Going anti-clockwise from O to U (4 → 3 → 2), S is between them. Yes. (Going clockwise, K, T, A are between them, but "between" usually implies the shorter path in puzzles unless specified).
• T (6) is immediate right of K (5)? Right of 5 is 6. Yes.
• Two persons between O (4) and A (1)? Going anti-clockwise from O to A (4 → 3 → 2 → 1), S and U are between them. Going clockwise (4 → 5 → 6 → 1), K and T are between them. Yes, satisfied by the opposite condition.

So the final seating arrangement in clockwise order is A, U, S, O, K, T.

Finding the Person Third to the Left of K

The arrangement is A, U, S, O, K, T in clockwise order.

We need to find the person third to the left of K. Left is anti-clockwise.

• K is at position 5.
• 1st person to the left of K (at 5) is the person at position 4, which is O.
• 2nd person to the left of K (at 5) is the person at position 3, which is S.
• 3rd person to the left of K (at 5) is the person at position 2, which is U.

Therefore, U is sitting third to the left of K.

Conclusion

Based on the step-by-step deduction from the given clues, the person sitting third to the left of K is U.

Revision Table: Key Clues and Deductions

Additional Information: Tips for Circular Arrangement Puzzles

Solving circular seating arrangement puzzles requires careful reading and logical deduction. Here are some tips:

• Start with the most definitive clues, like "opposite" or fixed relative positions.
• Use diagrams or numbered positions to keep track of the arrangement as you deduce it.
• Pay attention to "left" and "right" directions, remembering they are relative to the person facing the centre (or outside).
• If a clue presents multiple possibilities, explore each possibility systematically until one fits all clues and others are eliminated.
• The term "between" in circular arrangements usually refers to the shorter arc unless specified otherwise.