For which can an -sided polygon be made by joining several one-by-one squares together edge-to-edge? For instance, the given diagram shows an -sided polygon formed in this way. Note that a shape with holes is not a polygon and should not be considered.
This is an Olympiad problem, so you must show that all such values of are achievable, and that no other values are.
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Junior Mathematical Olympiad 2025 (2025)
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