Question

If Ankit puts E, H and M on the 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 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 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 \(O\) cannot be in the centre of the west wall. 
Other options are not forced by the conditions. \[ \boxed{\text{(b)}} \]