Question

Which of the following is \emph{not possible (respecting the O–E and O–T adjacency bans)?}

• A. T and O to be opposite to each other
• B. T, H and E to be on the same wall
• C. H, M and R to be on the same wall
• D. M and O to be opposite to each other

Hint:

Whenever one item (here \(O\)) is forbidden next to two others, that item cannot share a 3-slot wall with both of them.

Answer 1

The Correct Option is C

Step 1: Check each scenario.
(a) \(T\) opposite \(O\): place \(O\) on one wall, \(T\) facing it on the other—no same-wall adjacency involved—\textit{possible}.
(b) \(T,H,E\) on one wall: arrange as \(H\text{–}E\text{–}T\) (or any order avoiding a common word); the other wall gets \(M,O,R\) with \(O\) between \(M,R\)—\textit{possible}.
(d) \(M\) opposite \(O\): trivially \textit{possible}. Step 2: Why (c) is impossible.
If \(\{H,M,R\}\) occupy one wall, the other wall must be \(\{E,O,T\}\). On a 3-slot wall, the letter in the middle is adjacent to \emph{both} ends; whichever position \(O\) takes, it becomes adjacent to at least one of \(E\) or \(T\), violating both bans simultaneously (centre: adjacent to both; end: adjacent to the middle which must be \(E\) or \(T\)). Hence such a distribution cannot satisfy the constraints. \[ \boxed{\text{(c)}} \]