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

In this letter-to-number coding pattern, each letter is replaced by the square of its own position in the English alphabet (A = 1, B = 2, C = 3, ... Z = 26), and the resulting squares are written one after another — concatenated as digit strings, not added — to form the coded number.

Applying this to the two given examples:

1. ACE: A is the 1st letter, C is the 3rd letter, E is the 5th letter. Squaring each position gives 12 = 1, 32 = 9, 52 = 25. Writing these one after another gives 1925, matching the given code for ACE.

2. FAD: F is the 6th letter, A is the 1st letter, D is the 4th letter. Squaring each position gives 62 = 36, 12 = 1, 42 = 16. Writing these one after another gives 36116, matching the given code for FAD.

3. DIE: D is the 4th letter, I is the 9th letter, E is the 5th letter. Squaring each position gives 42 = 16, 92 = 81, 52 = 25. Writing these one after another gives 168125.

Cross-check: splitting 168125 back into 16, 81, and 25 gives three perfect squares whose square roots are 4, 9, and 5 — exactly the alphabet positions of D, I, and E in order — which is consistent with the same rule verified by both ACE and FAD.

So DIE is coded as 168125.