In a particular substitution, TEACHER is written as ZYXDOYK and RAIL as KXQM. Using the same one-to-one letter mapping, how is CHAIR written?

Introduction / Context:
This is a monoalphabetic substitution puzzle. Two examples provide enough letter pairs to deduce the mapping required to encode a new word consistently.

Given Data / Assumptions:

• TEACHER → ZYXDOYK gives mappings: T→Z, E→Y, A→X, C→D, H→O, R→K.
• RAIL → KXQM supplies: R→K (confirms), A→X (confirms), I→Q, L→M.
• One-to-one mapping; no position-based changes.

Concept / Approach:
Compile the mapping dictionary from the examples, then encode the target word by direct substitution character by character.

Step-by-Step Solution:
c → D (from TEACHER)h → O (from TEACHER)a → X (from both examples)i → Q (from RAIL)r → K (from both examples)Therefore, chair → DOXQK.

Verification / Alternative check:
Cross-check that every letter used in CHAIR has an established unique mapping from the examples, ensuring consistency.

Why Other Options Are Wrong:

• DOQXK / DOKQX / DQOXK: These involve letter-order swaps that contradict the strict per-letter substitution order derived from the mapping.

Common Pitfalls:
Inferring shifts or pair swaps instead of a fixed substitution; changing the order of letters rather than mapping each in place.

Final Answer:
DOXQK