Question

If he decides to celebrate by making the sequence around the room spell MOTHER, starting at the leftmost on the east wall and then going around the room, which of the following will be false?

• A. O is opposite to E
• B. H is next to E
• C. T is next to O
• D. T is opposite to R

Hint:

For opposite walls, the facing pairs are \((E_1,W_1), (E_2,W_2), (E_3,W_3)\). Use this fixed pairing to verify "opposite" claims quickly.

Answer 1

The Correct Option is D

Step 1: Map "going around the room".
Order of slots around the room: \(E_1,E_2,E_3,W_3,W_2,W_1\).
Placing \(\text{MOTHER}\) gives:
\(E_1=M,\ E_2=O,\ E_3=T,\ W_3=H,\ W_2=E,\ W_1=R\).

Step 2: Read opposites and adjacencies.
Opposites: \(E_1\leftrightarrow W_1: M\leftrightarrow R\),
\(E_2\leftrightarrow W_2: O\leftrightarrow E\),
\(E_3\leftrightarrow W_3: T\leftrightarrow H\).
Adjacencies (same wall): \(M\)-\(O\), \(O\)-\(T\) on east; \(R\)-\(E\), \(E\)-\(H\) on west.

Step 3: Test the options.
(a) \(O\) opposite \(E\): True.
(b) \(H\) next to \(E\): True.
(c) \(T\) next to \(O\): True.
(d) \(T\) opposite \(R\): False (since \(T\) is opposite \(H\)). \[ \boxed{\text{(d)}} \]