Gear Loops

Level pending

Here we see on the back of a two pound coin nineteen gears all linked in a "gear loop". Let us say that there are \(n\) gears in a certain "gear loop". What is the requirement for \(n\) such that all the gears can turn (they can all mesh)?

Clarification: All gears turning means that if we turn one gear clockwise, the entire system will move.

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