Question

If Ankit puts E, H and M on the \emph{east wall, which of the following must be true?}

• A. R and M cannot face each other
• B. O cannot be in the centre of the west wall
• C. E cannot be in the centre of the east wall
• D. T and M cannot face each other

Hint:

On a 3-slot line, "X cannot be next to Y" forces X and Y to be at the \emph{ends} with the third symbol fixed in the middle.

Answer 1

The Correct Option is B

Step 1: Fix the sets by wall.
East wall already contains \(\{E,H,M\}\) (in some order). Therefore the west wall must contain the remaining \(\{O,R,T\}\). Step 2: Apply the adjacency bans on the west wall.
On a 3-slot wall, the centre is adjacent to both ends. Since \(O\) cannot be adjacent to \(T\), \(O\) and \(T\) must be \emph{separated} by \(R\). Thus the only possible west orders are \(O\!-\!R\!-\!T\) or \(T\!-\!R\!-\!O\). In both, the centre is \(R\), never \(O\). Step 3: Conclude.
Hence \(O\) \emph{cannot} be in the centre of the west wall. Other options are not forced by the conditions. \[ \boxed{\text{(b)}} \]