If 125 is coded as VYZ and 487 is coded as TSW, then the code for 369 is:

Concept — In a number-to-letter code, test two independent features: the digit-to-letter mapping and the order in which the mapped letters are written. A common candidate mapping counts alphabet positions from the start (A = 1, B = 2 and so on) or from the end (Z = 1, Y = 2 and so on, so a digit d maps to position 27 - d); the output order may preserve or reverse the digit order. Decode every given clue letter by letter to identify which candidate rule fits all clues before applying it to a new number.

Applying it to this code

1. Decode the first clue with the from-the-end map: V is the 5th letter from the end (Z, Y, X, W, V), Y is the 2nd and Z is the 1st, so VYZ reads as 5, 2, 1.

2. Those are the digits of 125 in reverse order, so this code maps every digit to its letter counted from the end and writes those letters back to front.

3. Test the same rule on the second clue: T is the 7th letter from the end, S the 8th and W the 4th, so TSW reads as 7, 8, 4, which is 487 reversed. The rule survives the check.

4. Reverse the digits of the new number 369 to get 9, 6, 3.

5. Convert each of those digits to its letter counted from the end: 9 gives R, 6 gives U and 3 gives X.

6. So the code for 369 is RUX.

Digit to letter, counting from the end of the alphabet

Cross-check and the near misses

• Re-encode to confirm: RUX reads as 9, 6, 3, and reversing 9, 6, 3 gives back 369.

• XUR reads as 3, 6, 9, the digits in their given order, which is what the same letter map produces when the reversal that both clues demand is skipped.

• XRU reads as 3, 9, 6, the first digit left in place with only the last two swapped, so the order is neither the given one nor its full reverse.

• RXU reads as 9, 3, 6, which is not the reverse of 3, 6, 9.