If in a certain code, 1925 is written as ACE and 36116 is written as FAD, how…

Concept

In letter-to-number coding, each letter of a word is first replaced by its position in the English alphabet (A=1, B=2, ... Z=26), and that position is then transformed by a fixed rule (here, squared). The resulting numbers are written one after another, in the same left-to-right order as the letters, with no separator between them.

Application

Confirm the rule from the two given examples, then apply it to DIE:

1. ACE: A is the 1st letter -> 12 = 1; C is the 3rd letter -> 32 = 9; E is the 5th letter -> 52 = 25. Writing these one after another gives 1, 9, 25 -> “1925”, which matches the code given for ACE.

2. FAD: F is the 6th letter -> 62 = 36; A is the 1st letter -> 12 = 1; D is the 4th letter -> 42 = 16. Writing these one after another gives 36, 1, 16 -> “36116”, which matches the code given for FAD.

3. DIE: D is the 4th letter -> 42 = 16; I is the 9th letter -> 92 = 81; E is the 5th letter -> 52 = 25. Writing these one after another (D, then I, then E) gives 16, 81, 25 -> “168125”.

Cross-check

Reverse the process on “168125”: split it into three two-digit groups in order -> 16, 81, 25. Each is a perfect square (42, 92, 52), and the corresponding positions 4, 9, 5 map back to the letters D, I, E -- exactly the word being coded. This independently confirms the code is consistent with the rule used for both ACE and FAD.