J, K, L, M, O and P are sitting around a circular table facing the centre. Both L and M are immediate neighbours of J. Only one person sits between M and P. O sits second to the right of J. O is not an immediate neighbour of L. Who is sitting to the immediate right of K?

Let us solve this seating arrangement puzzle step-by-step.

There are 6 people: J, K, L, M, O, and P sitting around a circular table facing the centre. Facing the centre means that for any person, "left" is in the clockwise direction and "right" is in the anticlockwise direction.

Let's place the people step-by-step:
1. Both L and M are immediate neighbours of J: This means J is between L and M. So, we have two possible arrangements for this trio:
- Case 1: L is to the immediate left of J, and M is to the immediate right of J (clockwise: L - J - M).
- Case 2: M is to the immediate left of J, and L is to the immediate right of J (clockwise: M - J - L).

2. O sits second to the right of J: Counting two positions to the right (anticlockwise) from J, we place O. Since J is at some position, the person to the immediate right of J is at position 1 to the right, and the person second to the right of J is at position 2 to the right. Therefore, O sits second to the right of J.

3. O is not an immediate neighbour of L: Let's check our two cases:
- In Case 1 (clockwise: L - J - M): The person to the immediate right of J is M. The person second to the right of J (which is O) is next to M. In a 6-seat circle, the seats clockwise are L (1st), J (2nd), M (3rd), O (4th, which is second to the right of J). The remaining seats are 5th and 6th. Here, O is at position 4, and L is at position 1. They are separated by J (2nd) and M (3rd) on one side, and the 5th and 6th seats on the other. Thus, O and L are not adjacent.
- In Case 2 (clockwise: M - J - L): The person to the immediate right of J is L. The person second to the right of J is O. This means O must sit immediately to the right of L (since L is first to the right of J, and O is second to the right of J). This makes O and L immediate neighbours, which violates the condition "O is not an immediate neighbour of L". Therefore, Case 2 is invalid.

4. Let us proceed with Case 1 (clockwise order starting from L):
- Position 1: L
- Position 2: J
- Position 3: M
- Position 4: O (second to the right of J)
- This leaves Position 5 and Position 6 to be filled by K and P.

5. Only one person sits between M and P: M is at Position 3. The positions that have only one person between them and M are Position 1 (L is between M and Position 1 going clockwise, but Position 1 is already occupied by L) and Position 5 (O is between M and Position 5 going anticlockwise). Since Position 5 is vacant, P must sit at Position 5.

6. Remaining Person: The only remaining person is K, who must sit at the only remaining vacant seat, which is Position 6.

Let's verify the full clockwise arrangement:
L (Position 1) → J (Position 2) → M (Position 3) → O (Position 4) → P (Position 5) → K (Position 6) → L (Position 1).

Let us check all conditions with this final arrangement:
- L and M are immediate neighbours of J: Yes, J is between L and M.
- Only one person sits between M and P: Yes, O sits between M and P.
- O sits second to the right of J: Yes, going anticlockwise (right) from J (Position 2), the first right is M (Position 3) and the second right is O (Position 4).
- O is not an immediate neighbour of L: Yes, O is at Position 4 and L is at Position 1.
- All conditions are satisfied.

Now, we find who is sitting to the immediate right of K:
- K is at Position 6.
- The immediate right of K (anticlockwise direction) is Position 1, which is occupied by L.

Therefore, L is sitting to the immediate right of K.