Nine cricket fans are watching a match in a stadium. Seated in one row, they are J, K, L, M, N, O, P, Q and R. L is at the right of M and at third place at the right of N. K is at the end of the row. Q is seated adjacent to both O and P. O is at the third place at the left of K. J is right next to the left of O.
Who is sitting at the centre of the row?

Let's systematically reconstruct the single-row linear arrangement of the 9 positions ($1$ to $9$ from left to right):
1. "K is at the end of the row" and "O is at the third place to the left of K". This tells us K must be at the extreme right end (position 9) because if K were on the left end, we couldn't go left of it.
* Position 9: K

2. "O is at the third place at the left of K" $\to$ Position $=9-3=6$.
* Position 6: O

3. "J is right next to the left of O" $\to$ Position 5.
* Position 5: J

4. "Q is seated adjacent to both O and P". Since J is to the left of O, Q must be on the right side of O (position 7), and P follows next to Q (position 8).
* Position 7: Q
* Position 8: P
* Current right segment layout: _ _ _ _ J O Q P K

5. Now look at the left segment conditions: "L is at third place at the right of N" $\to \text{N}\_\_\text{L}$. Also, "L is at the right of M", meaning M must be exactly adjacent to the left of L $\to \text{N}\_\text{M L}$.
6. These four people must fit into the remaining available slots at the left (positions 1, 2, 3, 4):
* Position 1: N
* Position 2: R (the only unplaced person)
* Position 3: M
* Position 4: L

The complete linear arrangement from left to right is:

$$\text{1:N, 2:R, 3:M, 4:L, 5:J, 6:O, 7:Q, 8:P, 9:K}$$

The center position of a 9-person row is the $5^{\text{th}}$ slot, which is occupied by J.