Pattern decoding — Given 4 − 4 = 17, 6 − 6 = 37, 2 − 2 = 5, find the value of 5 − 5

Introduction / Context:These items encode a number transformation rather than ordinary subtraction. We must infer the hidden rule consistent with the examples and apply it to 5 − 5.

Given Data / Assumptions:

• 4 − 4 = 17, 6 − 6 = 37, 2 − 2 = 5.

Concept / Approach:Observe that n − n maps to n^2 + 1: 4^2+1=17, 6^2+1=37, 2^2+1=5. The same rule applied to n=5 yields 5^2+1=26.

Step-by-Step Solution:

Verification / Alternative check:Try alternate simple forms (e.g., 2n+9); they do not fit all three examples, reinforcing n^2+1.

Why Other Options Are Wrong:

• 27/24/20 do not match the consistent quadratic pattern across the exemplars.

Common Pitfalls:

• Assuming standard subtraction instead of a coded rule.

Final Answer:26