Consistent letter→digit substitution: Given “GLOSSORY” = 97533562 and “GEOGRAPHY” = 915968402, determine the code for “GEOLOGY”.

Introduction / Context:
This problem uses a direct letter→digit substitution that must stay consistent across two examples. By extracting a complete mapping for the letters that appear, we can encode a new word unambiguously.

Given Data / Assumptions:

• “GLOSSORY” = 9 7 5 3 3 5 6 2
• “GEOGRAPHY” = 9 1 5 9 6 8 4 0 2
• Target word: “GEOLOGY”.

Concept / Approach:
Build a map letter→digit from both given encodings and verify consistency. Then transcribe each letter of GEOLOGY using that map.

Step-by-Step Solution:

Verification / Alternative check:
Cross-check every letter in GEOLOGY appears in the map and is consistent across both given words (notably G, O, Y are present in both exemplars). No conflict arises.

Why Other Options Are Wrong:

• 915692 / 9057592 / 9157591: Each alters at least one mapped digit (e.g., L or H/Y positions) contradicting the established map.
• None of these: Not applicable because 9157592 matches exactly.

Common Pitfalls:
Assuming position-based coding rather than a pure substitution; mixing digits for already-mapped letters; failing to consolidate both exemplars before encoding the target.

Final Answer:
9157592