In a certain coding language if the word 'SOUND' is coded as 'VLXKG', then the…

Concept

In a letter-shift code every letter of a word is replaced by the letter standing a fixed number of places away in the alphabet, and the direction of that displacement may alternate from one position to the next. The rule is recovered by writing both the given word and its code as alphabet position numbers (A = 1, B = 2, … Z = 26) and reading the signed difference at each position; those same signed differences are then applied to the target word.

Application

1. Number the given pair: SOUND = 19, 15, 21, 14, 4 and VLXKG = 22, 12, 24, 11, 7.

2. Subtract position by position: 22 − 19 = +3, 12 − 15 = −3, 24 − 21 = +3, 11 − 14 = −3, 7 − 4 = +3. The rule is therefore the alternating shift +3, −3, +3, −3, +3.

3. Number the target word: TRAIN = 20, 18, 1, 9, 14.

4. Apply the same signed shifts: 20 + 3 = 23, 18 − 3 = 15, 1 + 3 = 4, 9 − 3 = 6, 14 + 3 = 17.

5. Convert the results back to letters: 23 = W, 15 = O, 4 = D, 6 = F, 17 = Q, so TRAIN is coded as WODFQ.

Cross-check

Reversing the rule on WODFQ with the opposite shifts −3, +3, −3, +3, −3 gives 23 − 3 = 20, 15 + 3 = 18, 4 − 3 = 1, 6 + 3 = 9 and 17 − 3 = 14, which reads T, R, A, I, N. The coding is therefore consistent in both directions.

Contrast

Measured against TRAIN, the remaining strings do not keep the alternating step of 3:

• VQWPF uses the shifts +2, −1, −4, +7, −8.

• WQDGQ uses the shifts +3, −1, +3, −2, +3.

• VODGQ uses the shifts +2, −3, +3, −2, +3.