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.