A bottle of Cotnari

Geometry Level pending

The figure above represents a curve drawn on a cilindric surface and is called helix. The distance between two consecutive points of a helix placed on the same axis is constant \( AD\equiv BE\equiv CF\equiv DH\equiv FK\equiv GL\equiv \ldots \) and is called pitch.

The pitch of a corkscrew's helix is \(8\text{ mm} \) and the length of a cork is \(4\text{ cm} \). A man who tries to open a bottle of COTNARI can spin his hand for only 120 degrees. How many moves are required so that the the corkscrew passes through the cork?

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