Infer the rule from examples: 12 (169) 5, 4 (20) 2, and 1 (26) 5. Compute the missing middle value for 7 (?) 3.

Introduction / Context:
This is a classic “find the rule” puzzle where the middle value in parentheses is derived from the two outer numbers using a consistent operation. Once the pattern is recognized, apply it to the target pair to compute the missing value.

Given Data / Assumptions:

• 12 (169) 5
• 4 (20) 2
• 1 (26) 5
• Query: 7 (?) 3

Concept / Approach:
A compact, natural rule fitting all three examples is: middle = left^2 + right^2. This uses perfect squares, which are common in such reasoning items.

Step-by-Step Solution:
Check with 12 (169) 5: 12^2 + 5^2 = 144 + 25 = 169 ✅Check with 4 (20) 2: 4^2 + 2^2 = 16 + 4 = 20 ✅Check with 1 (26) 5: 1^2 + 5^2 = 1 + 25 = 26 ✅Apply to 7 (?) 3: 7^2 + 3^2 = 49 + 9 = 58.

Verification / Alternative check:
Other simple rules (like multiplication or concatenation) fail at least one given example, whereas the sum-of-squares rule satisfies all three, making it the intended pattern.

Why Other Options Are Wrong:
78, 68, and 36 correspond to misreading the rule as 7 × (something), 7 concatenated with 8 or 6, or 6^2, none of which matches the consistent square-sum pattern.

Common Pitfalls:

• Using (left + right)^2 instead of left^2 + right^2.
• Attempting left × right or left^right, which do not fit all exemplars.

Final Answer:
58.