Enigma

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Enigma is a rotational/rearrangement puzzle. Comprised by three layers, you rotate these to scramble or rearrange the puzzle to its original picture. The top layer rotates only four circles and the second center ring (see first bottom picture), whilst the bottom layer rotates all the parts.

This puzzle is usually available with a company's logo, because they only make them as promotional items and sell them as wholesale.

As of writing this article, there's an eBay seller with over 80 enigma puzzles available in 6 designs/logos. He also has a video that shows how the puzzle moves.

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Links:

Jaap's Puzzle Page (Solution) 

TwistyPuzzles.com (More information)

TwistyPuzzles.com (Mechanism)