Analogy — Complete the relation by preserving the exact rule used in the model pair: 41537 is related to 4 in the same way as 421 is related to ____.

Introduction / Context:
This numeric analogy asks you to infer a rule from the mapping 41537 → 4 and then apply the same rule to 421. The goal is to keep the identical transformation, not invent a new one for the second number.

Given Data / Assumptions:

• Model: 41537 maps to 4.
• Target: 421 maps to ? using the same rule.
• We seek a simple, digit-based rule that is consistent and reproducible.

Concept / Approach:
A compact and consistent rule is to count the number of odd digits in the numeral. For 41537, the odd digits are 1, 5, 3, 7 — exactly four odd digits — which yields 4. We must apply this same rule to 421.

Step-by-Step Solution:

Verification / Alternative check:
The rule “number of odd digits” is minimal, deterministic, and uses only local digit properties. It exactly reproduces the model mapping and gives an unambiguous result for 421.

Why Other Options Are Wrong:

• 2, 3, 4 — these would require changing the rule used for 41537.
• None of these — incorrect because a consistent, simple rule produces 1.

Common Pitfalls:
Switching to a new rule for the second number or using operations that work for one example but fail the model.

Final Answer:
1