Question

A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters.
\[ \boxed{A} \qquad \boxed{D} \] From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome? The player should use all the five plates exactly once. The plates can be rotated in their plane.

• A. \(\boxed{D} \quad \boxed{\rotatebox[origin=c]{180}{D}} \quad \boxed{J}\)
• B. \(\boxed{R} \quad \boxed{\rotatebox[origin=c]{180}{A}} \quad \boxed{R}\)
• C. \(\boxed{Z} \quad \boxed{\rotatebox[origin=c]{180}{E}} \quad \boxed{D}\)
• D. \(\boxed{I} \quad \boxed{\rotatebox[origin=c]{180}{L}} \quad \boxed{Y}\)

Hint:

To form a palindrome, always check whether pairs of letters can match or remain identical when rotated.

Answer 1

The Correct Option is B

Step 1: Requirements for a 5-letter palindrome.
A 5-letter palindrome has the structure: \[ x \; y \; z \; y \; x \] Thus, letters in positions 1 and 5 must match, and letters in positions 2 and 4 must match. The middle letter (position 3) can be anything. Step 2: Given plates.
The player already has: \(A\) and \(D\). To build a 5-letter palindrome, we need pairs of matching letters OR letters that look identical when rotated. Step 3: Check each option.
(A) Contains \(D, D, J\). Two matching D’s exist, but J cannot form any symmetric pair with A or D. Not usable. (B) Contains \(R, A(\text{rotated}), R\). The rotated \(A\) still appears as \(A\). We now have:
- \(A\) (from original)
- \(A\) (rotated plate)
- \(R, R\)
- plus the given \(D\)
This gives enough symmetric pairing:
Example palindrome: \(R \; A \; D \; A \; R\). (C) Contains \(Z, E(rotated), D\). This cannot form symmetric pairs with A and D correctly. (D) Contains \(I, L(rotated), Y\). These letters cannot form the required pairs. Thus, only option (B) allows a valid 5-letter palindrome.