Classification – Odd one out (cube ± 1 pattern) Three numbers follow the pattern n^3 + 1 for consecutive integers n = 3, 4, 5. Identify the number that does not follow n^3 + 1 and mark it as the odd one out.

Introduction / Context:
Recognizing hidden formulas is central to many classification puzzles. Here, three values are exactly one more than perfect cubes for consecutive n, while one value breaks that formulaic rule.

Given Data / Assumptions:

• Options: 28, 65, 126, 215
• Suspected pattern: n^3 + 1 for successive n

Concept / Approach:
Compute nearby cubes and compare: 3^3 = 27, 4^3 = 64, 5^3 = 125, 6^3 = 216. Add 1 to each and match with the options.

Step-by-Step Solution:
3^3 + 1 = 27 + 1 = 28 → present.4^3 + 1 = 64 + 1 = 65 → present.5^3 + 1 = 125 + 1 = 126 → present.6^3 + 1 = 216 + 1 = 217 → not present; instead we have 215 = 216 - 1 = 6^3 - 1.

Verification / Alternative check:
The three conformers are one more than consecutive cubes (n = 3, 4, 5). The misfit, 215, is one less than 6^3, confirming it violates the n^3 + 1 rule.

Why Other Options Are Wrong:

• 28: Fits 3^3 + 1.
• 65: Fits 4^3 + 1.
• 126: Fits 5^3 + 1.
• None of these: There is a clear odd one (215).

Common Pitfalls:
Matching loosely to “near a cube” without checking whether it is +1 or -1. Always verify the exact relation.

Final Answer:
215