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What is higher without the head, than with it?

Illustration for riddle: What is higher without the head, than with it?

Common Wrong Answers

A mountain

A mountain is not higher without its peak; it maintains its height regardless of any weight placed upon it.

A roof

A roof does not change its height based on whether something is on top of it; it remains constant.

A flagpole

A flagpole's height remains the same regardless of whether a flag is at the top, making it not applicable to the riddle.