A palindrome is a word that reads the same forwards and backwards. In a game…
2022
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.
Attempted by 45 students.
Show answer & explanation
Key idea: A five-letter palindrome needs the first and last letters to match, the second and fourth letters to match, and any letter in the middle. Rotation of plates is allowed, so a rotated letter still counts as that letter.
Look at the available plates when choosing the additional plates that show R, A (rotated), and R.
Combining those with the existing A and D gives the multiset of letters: R, R, A, A, D (two Rs, two As, one D).
Arrange them as R A D A R; this uses every plate exactly once and reads the same forwards and backwards, so RADAR is a valid palindrome.
Why the other additional-plate sets fail:
Set with D, rotated D, and J: letters become A, D, D, D, J — there are three Ds and two unique single letters, so you cannot form the two matching pairs needed for positions 1&5 and 2&4.
Set with Z, rotated E, and D: letters become A, D, Z, E, D — only the Ds pair; the remaining three letters are all different, so a symmetric arrangement is not possible.
Set with I, rotated L, and Y: letters become A, D, I, L, Y — no letter repeats, so you cannot form the required matching pairs.
Final palindrome: RADAR
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