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.
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.

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.

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.

Prepp Team · Accepted Answer

Problem AnalysisThe goal is to construct a 5-letter palindrome using two initial plates, A and D, and one of the provided sets of three additional plates. A palindrome is a word that reads the same forwards and backwards (e.g., $ \text{RADAR} $).A crucial rule is that the plates can be rotated in their plane. This allows us to reorient letters to their standard form or potentially transform them into other characters.Step-by-Step Solution1. Identify the Palindrome StructureA five-letter palindrome follows the pattern $ L_1 L_2 L_3 L_2 L_1 $. This means we need:Two pairs of identical letters ($ L_1 $ and $ L_2 $).One unique middle letter ($ L_3 $).We already have the letters A and D.2. Evaluate Option (B)Let's examine the plates in Option (B):First plate: The letter R.Second plate: An upside-down A. Rotating this $ 180^\circ $ in its plane results in the letter A.Third plate: A rotated R. Rotating this $ 180^\circ $ in its plane results in the letter R.By rotating these plates, we obtain the letters: $ \{R, A, R\} $.3. Combine All PlatesCombining the original plates with the rotated plates from Option (B), we have the following set of five letters: $$ \{A, D\} \cup \{R, A, R\} = \{R, A, D, A, R\} $$4. Construct the PalindromeUsing these five letters exactly once, we can form the word: $$ \mathbf{R \text{ — } A \text{ — } D \text{ — } A \text{ — } R} $$ This word is a valid five-letter palindrome.ConclusionOption (B) provides the necessary letters (after rotation) to complement the initial "A" and "D" plates and form the palindrome RADAR.Final Answer: The correct combination is (B).