Certain number of people are sitting in a row such that all of them a...
T is seventh from any of the extreme ends of the row.
Here T can be possible in two places which are given below in Case(i) and Case(ii).
Case(i)
(end) _ _ _ _ _ _ T
Case(ii)
T _ _ _ _ _ _ (end)
Three people are sitting between T and F who is second to the left of W.
In each case F is possible in two places which are given below in Case(i)(a), Case(i)(b), Case(ii)(a) and Case(ii)(b).
Case(i)(a)
(end) _ _ F _ W _ T
Case(i)(b)
(end) _ _ _ _ _ _ T _ _ _ F _ W
Case(ii)(a)
T _ _ _ F _ W (end)
Case(ii)(b)
F _ W _ T _ _ _ _ _ _ (end)
Five people are sitting between W and Q who is third to the right of B.
In Case(ii)(a), Q is not possible as per the above given condition. So this case is eliminated.
In Case(ii)(b), Q is possible in two places which are given below in Case(ii)(b)(1) and Case(ii)(b)(2).
Case(i)(a)
(end) _ _ F _ W _ T B _ _ Q
Case(i)(b)
(end) _ _ _ _ _ _ T _ _ _ F _ W _ _ B _ _ Q
Case(ii)(b)(1)
F _ W _ T B _ _ Q _ _ (end)
Case(ii)(b)(2)
B _ _ Q _ _ _ F _ W _ T _ _ _ _ _ _ (end)
B is immediately right of K.
In Case(i)(a) and Case(ii)(b)(1), K is not possible as per the above given condition. So this case is eliminated.
Case(i)(b)
(end) _ _ _ _ _ _ T _ _ _ F _ W _ K B _ _ Q
Case(ii)(b)(2)
K B _ _ Q _ _ _ F _ W _ T _ _ _ _ _ _ (end)
One person is sitting between K and P. M sits exactly between P and F.
In Case(ii)(b)(2), P is possible in two places which are given below in Case(ii)(b)(2)(i) and Case(ii)(b)(2)(ii).
Case(i)(b)
(end) _ _ _ _ _ _ T _ _ _ F _ W M K B P _ Q
Case(ii)(b)(2)(i)
K B P _ Q M _ _ F _ W _ T _ _ _ _ _ _ (end)
Case(ii)(b)(2)(ii)
P_ K B _ M Q _ _ _ F _ W _ T _ _ _ _ _ _ (end)
M and J are immediate neighbours of each other. The number of people sitting between M and B is the same as the number of people sitting between M and C. Three people are sitting between C and S.
In Case(i)(b), J is not possible as per the above given condition. So this case is eliminated.
Case(ii)(b)(2)(i)
K B P _ Q M J _ F C W _ T S _ _ _ _ _ (end)
Case(ii)(b)(2)(ii)
P_ K B J M Q C _ _ F S W _ T _ _ _ _ _ _ (end)
The number of people sitting to the left of B and right of S is the same.
Case(ii)(b)(2)(i)
(end) _ _ _ _ K B P _ Q M J _ F C W _ T S _ _ _ _ _ (end)
Case(ii)(b)(2)(ii)
(end) _ _ _ _ _ _ P_ K B J M Q C _ _ F S W _ T _ _ _ _ _ _ (end)
Six people are sitting between S and D.
In Case(ii)(b)(2)(i), D is not possible as per the above given condition. So this case is eliminated.
Case(ii)(b)(2)(ii)
(end) _ _ _ _ _ _ P_ K B J M Q C _ _ F S W _ T _ _ _ D _ _ (end)
A and D are immediate neighbours of each other. Three people are sitting together between A and R.
In Case(ii)(b)(2)(ii), A is possible in two places which are given below in Case(ii)(b)(2)(ii)(1) and Case(ii)(b)(2)(ii)(2).
Case(ii)(b)(2)(ii)(1)
(end) _ _ _ _ _ _ P_ K B J M Q C _ _ F S W R T _ _ A D _ _ (end)
Case(ii)(b)(2)(ii)(2)
(end) _ _ _ _ _ _ P_ K B J M Q C _ _ F S W _ T R _ _ D A _ (end)
R is fourth to the right of N. The number of people sitting between N and J is the same as the number of people sitting between J and Z.
In Case(ii)(b)(2)(ii)(2), N is not possible as per the above given condition. So this case is eliminated.
Case(ii)(b)(2)(ii)(1)
(end) _ _ _ _ _ Z P_ K B J M Q C _ N F S W R T _ _ A D _ _ (end)
One person is sitting between Z and Y who is third to the right of U who doesn't sit at any of the extreme ends of the row.
Case(ii)(b)(2)(ii)(1)
(end) _ _ _ _ U Z P Y K B J M Q C _ N F S W R T _ _ A D _ _ (end)
The number of people sitting to the left of U and right of I is the same. Two people are sitting between I and L.
Case(ii)(b)(2)(ii)(1)
(end) _ _ _ _ U Z P Y K B J M Q C _ N F S W R T _ I A D L _ (end)
More than two people are sitting between Z and E. O and E are immediate neighbours of each other but none of them is sitting at any of the extreme end of the row.
(end) _ E O _ U Z P Y K B J M Q C _ N F S W R T _ I A D L _ (end)
Therefore, we got the final arrangement which is given above.
According to the above arrangement, four people can sit between A and W.