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

To find the correct combination of plates that results in a five-letter palindrome, let's first understand what a palindrome is. A palindrome is a sequence that reads the same forwards and backwards. Given the initial plates \(\boxed{A}\) and \(\boxed{D}\), we need to add three more letters from one of the options so that the entire sequence forms a palindrome consisting of five letters.

1. Assess each option to determine if they can form a palindrome with the given letters.
2. Start with the first option: \(\boxed{D}\), \(\boxed{\rotatebox[origin=c]{180}{D}}\), \(\boxed{J}\). Adding these to the existing letters:
   • Configuration: AD[D] J A
   • Reversing it gives: AJDDA
   • This does not match the original order (ADDJA), so it is not a palindrome.
3. Evaluate the second option: \(\boxed{R}\), \(\boxed{\rotatebox[origin=c]{180}{A}}\), \(\boxed{R}\):
   • Configuration: AD[R] A R
   • Reversing it gives: RARDA
   • Both the original (RADAR) and reversed order (RADAR) match, confirming this is a palindrome.
4. Check the third option: \(\boxed{Z}\), \(\boxed{\rotatebox[origin=c]{180}{E}}\), \(\boxed{D}\):
   • Configuration: AD[Z] E D
   • Reversing it gives: DEZDA
   • These do not match the sequence ADEZD, so it is not a palindrome.
5. Check the fourth option: \(\boxed{I}\), \(\boxed{\rotatebox[origin=c]{180}{L}}\), \(\boxed{Y}\):
   • Configuration: AD[I] L Y
   • Reversing it gives: YLIAD
   • Neither order matches the original order ADILY, it is not a palindrome.

Therefore, the only option that results in a palindrome is the second option.

The correct answer is: \\(\boxed{R} \quad \boxed{\rotatebox[origin=c]{180}{A}} \quad \boxed{R}\\)