Eleven people J, K, L, M, N, O, P, Q, R, S and T are sitting in a lin...
Five people are sitting between R and J which is second to the left of N.
Here four cases are possible as per the given condition which are given below in Case(i), Case(ii), Case(iii) and Case(iv).
Case(i) R _ _ _ _ _ J _ N(↑)
Case(ii) R _ _ _ N(↓) _ J
Case(iii) J _ N(↑) _ _ _ R
Case(iv) N(↓) _ J _ _ _ _ _ R
Q sits exactly between R and N.
Case(i) R _ _ _ Q _ J _ N(↑)
Case(ii) R _ Q _ N(↓) _ J
Case(iii) J _ N(↑) _ Q _ R
Case(iv) N(↓) _ J _ Q _ _ _ R
The number of people sitting between J and Q is the same as the number of people sitting between Q and T who is second to the right of K.
In Case(i) and Case(iv), after putting T, K is not possible as per the above given condition. So this case is eliminated.
Case(ii) K(↑) _ T _ R _ Q _ N(↓) _ J
Case(iii) J _ N(↑) _ Q _ R _ T _ K(↓)
K does not face the north direction.
In Case(ii), K faces the north direction which is not possible as per the above given condition. So this case is eliminated.
Case(iii) J _ N(↑) _ Q _ R _ T _ K(↓)
O is immediately left of T.
In Case(iii), T is possible in two places which are given below in Case(iii)(a) and Case(iii)(b).
Case(iii)(a) J _ N(↑) _ Q _ R O T(↑) _ K(↓)
Case(iii)(b) J _ N(↑) _ Q _ R _ T(↓) O K(↓)
More than three people are sitting between O and L.
In Case(iii)(b), L is possible in two places which are given below in Case(iii)(b)(1) and Case(iii)(b)(2).
Case(iii)(a) J L N(↑) _ Q _ R O T(↑) _ K(↓)
Case(iii)(b)(1) J _ N(↑) L Q _ R _ T(↓) O K(↓)
Case(iii)(b)(2) J L N(↑) _ Q _ R _ T(↓) O K(↓)
L who is second to the right of S. M and T are not immediate neighbours of each other.
In Case(iii)(b)(1), S is possible in two places which are given below in Case(iii)(b)(1)(i) and Case(iii)(b)(1)(ii).
Case(iii)(a) J L N(↑) S(↓) Q M R O T(↑) _ K(↓)
Case(iii)(b)(1)(i) J M N(↑) L Q S(↓) R _ T(↓) O K(↓)
Case(iii)(b)(1)(ii) J S(↑) N(↑) L Q M R _ T(↓) O K(↓)
Case(iii)(b)(2) J L N(↑) S(↓) Q M R _ T(↓) O K(↓)
Not more than one person is sitting between M and P.
In Case(iii)(a) and Case(iii)(b)(1)(i), P is not possible as per the above given condition. So this case is eliminated.
Case(iii)(b)(1)(ii) J S(↑) N(↑) L Q M R P T(↓) O K(↓)
Case(iii)(b)(2) J L N(↑) S(↓) Q M R P T(↓) O K(↓)
The immediate neighbours of S face opposite directions to each other.
Case(iii)(b)(1)(ii) J(↓) S(↑) N(↑) L Q M R P T(↓) O K(↓)
Case(iii)(b)(2) J L N(↑) S(↓) Q(↓) M R P T(↓) O K(↓)
As per the information given in the instructions, not more than two immediate neighbours face the same direction.
Case(iii)(b)(1)(ii) J(↓) S(↑) N(↑) L(↓) Q M R P T(↓) O(↑) K(↓)
Case(iii)(b)(2) J L N(↑) S(↓) Q(↓) M(↑) R P T(↓) O(↑) K(↓)
The direction of O and J is the same.
In Case(iii)(b)(1)(ii), the above given condition is not applicable. So this case is eliminated.
Case(iii)(b)(2) J(↑) L N(↑) S(↓) Q(↓) M(↑) R P T(↓) O(↑) K(↓)
The immediate neighbours of R face opposite directions to each other.
After that only the direction of L and R are remaining which we can determine from the instruction given in the question.
J(↑) L(↓) N(↑) S(↓) Q(↓) M(↑) R(↑) P(↓) T(↓) O(↑) K(↓)
Therefore, we got the final arrangement which is given above.
According to the above arrangement, if all the people are arranged in alphabetical order starting from left to right, then the position of one person (J) remains unchanged.