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Difficulty: MediumSeating Arrangement

Eight colleagues—K, L, M, N, O, P, Q, and R—are sitting around a square table. Four of them sit in the middle of the sides and face the center of the table, while the other four sit at the four corners and face outside (away from the center). They are seated according to the following conditions:

- M sits in the middle of one of the sides.
- K sits third to the left of M.
- Only two people sit between K and R.
- O sits to the immediate right of R.
- P sits second to the left of K.
- N is an immediate neighbor of O.
- Q sits to the immediate right of P.

Based on the given seating arrangement, which of the following statements are correct? (Select all that apply)

  1. L sits to the immediate right of M.Answer
  2. B
    R sits to the immediate left of O.
  3. C
    O sits second to the left of K.
  4. Exactly three people sit between K and L when counted from the right of K.Answer

Answer

The correct statements are that L sits to the immediate right of M, and exactly three people sit between K and L when counted from the right of K.
Based on the seating conditions, M is at a middle position (facing center). K is 3rd to the left (clockwise), placing K at a corner facing outside. R is separated from K by two people, meaning R is at the opposite middle position (facing center). O is to the immediate right of R (counter-clockwise), placing O at a corner facing outside. P is 2nd to the left of K (counter-clockwise), so P is at a corner. N is O's neighbor, leaving only one adjacent spot. Q is immediate right of P (clockwise). L takes the last spot. In this final layout, L is immediately counter-clockwise from M, which is M's right side, making the first statement correct. Counting clockwise from K (K's right side), we pass N, O, and R before reaching L, making the statement about three people between K and L correct.

Step-by-Step Solution

1
Determine M and K's positions.
M is at a middle position (facing center). K is 3rd to the left of M. Since M faces the center, left is clockwise, placing K at a corner (facing outside).
M is explicitly given as sitting in the middle. The direction rules (center = left is clockwise) determine K's placement.
2
Determine R and O's positions.
R must be at the opposite middle position (facing center). O is to the immediate right of R, placing O at the adjacent corner counter-clockwise (facing outside).
Only two people sit between K and R, so R is opposite M. R faces the center, so its right is counter-clockwise.
3
Place P, N, Q, and L.
P is 2nd to the left of K (counter-clockwise), N is the only available neighbor of O, Q is to the immediate right of P (clockwise), and L takes the final remaining position.
Following the remaining clues step-by-step while strictly adhering to the left/right rules for inward vs. outward facing positions ensures a unique arrangement.
4
Evaluate the given statements based on the final arrangement.
The statements about L's position relative to M, and the number of people between K and L (counting from K's right) are correct.
By applying the left/right rules to the completed seating layout, we can confirm the validity of each statement.

Key Concept

Polygonal Seating Arrangement with Mixed Facing Directions
Estimated Time:2m 0s
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Topics

Seating Arrangement

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