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This is a puzzle attributed to Lionel Penrose according to a Russian blog post (http://www.nesenenko.narod.ru/GOLDHAND/game3.html).

Is that true? I can't find proofs that this is his invention. Also, what is the name of this puzzle in English?

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The general term for this type of puzzle is a coordinate-motion puzzle.

I don't know when the three-part disc version of the puzzle was first made. In the US patent US4397466A for the Cerebral Rings puzzle by Mag-Nif I found the following text:

A disk type puzzle called the "Magic Disk" is shown and described in a book entitled "Creative Puzzles of the World" by Peter Van Delft and Jack Botermans 1978, page 70 (Harry N. Abrams Inc., Publishers). This puzzle is in the form of three identical wooden disks which have been tri-sected and the sections glued together in a special pattern. The disks may then be fitted together to form a geometric solid which has the appearance of three stacked disks. With the three disks assembled, they cannot be pulled apart by any amount of pulling or tugging. Only a force applied in a certain way can separate the three components forming the stacked disks.
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Another version of the puzzle was designed by Professor Lionel Penrose, and is sold by Pentangle Hampshire, England and is called "Pandora's Box". This version of the puzzle has a poker chip inside that says "Hope!" on it. This piece apparently serves as a reward for opening the puzzle, but it is also there to make the person working the puzzle believe that it is the only internal element. The fact is, there is a small metal dowel which locks the layers of the puzzle together so that nothing can be moved. The only way to open the puzzle is by holding the puzzle vertically and shaking it so that the pin can be positioned in the center layer. Solving this puzzle is more by luck than by skill on the part of the problem solver. Once completely disassembled, this puzzle is even more difficult to put back together.

The Pandora's Box puzzle was on the market in 1979, but possibly already earlier, especially given that Lionel Penrose died in 1972. Here is a picture of it taken from this site:

Pandora's Box

It could be that Lionel Penrose added an extra locking pin to the already pre-existing puzzle disc puzzle, though it is very possible he invented the original non-locking version too. Unfortunately I have not yet found any proof one way or the other, though this does at least establish that Penrose is associated with the puzzle.

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