In Certain code, PAPER is written as SCTGW. How is ‘MOTHER’ written in that…

Concept

In letter-shift coding puzzles, every letter of the key word is moved forward in the alphabet by a fixed number of places to get its code letter, but that shift amount is not always the same for every letter — it can follow its own sub-pattern across the word's positions. The first job is to work out the exact shift used at each position of the key word, spot how those shifts vary, and then apply that same rule, position by position, to the target word.

Application

1. Find the shift used for each letter of the key word PAPER → SCTGW (alphabet position of each letter, A = 1):

   • P (16) → S (19): shift +3

   • A (1) → C (3): shift +2

   • P (16) → T (20): shift +4

   • E (5) → G (7): shift +2

   • R (18) → W (23): shift +5

2. Read the pattern in these shifts by position — the 1st, 3rd and 5th letters (P, P, R) take an increasing shift of +3, +4, +5, while the 2nd and 4th letters (A, E) both take a flat shift of +2. So odd positions increase by one each time and even positions stay constant.

3. Apply the same rule to MOTHER, letter by letter:

   • M (13), 1st letter, odd → +3 → 16 → P

   • O (15), 2nd letter, even → +2 → 17 → Q

   • T (20), 3rd letter, odd → +4 → 24 → X

   • H (8), 4th letter, even → +2 → 10 → J

   • E (5), 5th letter, odd → +5 → 10 → J

   • R (18), 6th letter, even → +2 → 20 → T

4. Reading the code letters in order gives P Q X J J T → PQXJJT.

Cross-check

Reversing the check confirms it: subtracting the same shifts back from P, Q, X, J, J, T (−3, −2, −4, −2, −5, −2) returns 13, 15, 20, 8, 5, 18 — exactly M, O, T, H, E, R. The pattern that converts PAPER to SCTGW converts MOTHER to PQXJJT without any inconsistency.

Hence, MOTHER is coded as PQXJJT.