Number analogy – apply the rule (difference of digits)^2 14 : 9 :: 26 : ?

Introduction / Context:
Number analogies often hide a simple arithmetic rule applied to the digits. Here we identify a pattern that converts a two-digit number on the left to a single number on the right, then apply it to the second pair.

Given Data / Assumptions:

• 14 maps to 9.
• We need to determine 26 maps to ?
• Only digit-level operations are considered; no advanced functions are required.

Concept / Approach:
Try concise digit relations: sum, product, and especially the absolute difference. Notice that for 14, the absolute difference of digits is |4−1| = 3, and 3^2 = 9, which equals the right-hand value. So the rule appears to be: square of the digit difference.

Step-by-Step Solution:

Verification / Alternative check:
Check other examples mentally: the rule is consistent for pairs where the right side equals the square of the absolute digit difference. It is simple, symmetric (order of digits does not matter), and explains 14 → 9 perfectly.

Why Other Options Are Wrong:

• 12/13/15: None equals 4^2, which is required by the revealed pattern when applied to 26.

Common Pitfalls:
Using digit sum or product (which would give 5 or 8 + 12 combined) and overfitting complicated rules; ignoring that 14 clearly fits the squared-difference pattern.

Final Answer:
16