Solutions
Let the students be sitting from 1-8 in clockwise direction. Let us assume that V be sitting at 1, which implies P would be at 4. Now, P and T are neighbors, so T is at 3 or 5. No two adjacent persons face the centre implies the neighbors of V i.e. the person at 2 and 8 are not facing the centre. Now, if T is at 3, then the person at 1 and 5 are facing away from the centre, but we know that V is at 1and is facing the centre. Therefore, T is at 5 and the persons at 3 and 7 are facing away from the centre. W and Y are sitting opposite each other. Therefore, they are at (3,7) or (2,6) in any order. Now, U is second to the right of W and we know that W can be at 3, 7, 2 or 6. If W is at 2, 3 or 7, someone is already sitting second to the right of that position. Therefore, W is at 6 and is facing away from the centre. Therefore, U is at 8 and Y at 2. Now, X can be at 3 or 7, and we know the neighbors of X are facing in the opposite directions to each other. If X is at 7, then persons at 6 and 8 should be facing in the opposite direction, but that is not the case. Therefore, X is at 3 and that would mean P at 4 would be facing the centre, which also implies T at 5 would be facing away from the centre and Q would be at 7.
The Green box is represents the persons facing the centre and the red box represents the person facing away from the centre.
