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Disclaimer: I'm not a mathematican. Please answer in a way a non-mathematican can understand. Thank you.

I'm building kind of a wooden puzzle and got stuck. My problem is: I have squares whose 4 edges have x different key-and-slot-patterns. Each square looks the same. Now I can join different squares to each other (edge-to-edge) as long as the edges don't share the same key-and-slot-pattern. I prefer to see the keys and slots as a "color". That way each square has x colors whose edges can be joined to each other as long as their color differentiates. Joining may happen planar or perpendicular. In a first step I want to build a cube whose 6 faces consist out of 6 squares. I want to know how many different edge colors I need when building a) an ordinary cube b) a cube in cube system like the rubic's cube (3x3x3). Can anybody give me a tipp where to start?

Here's a picture of the "keys-and-slots" and the resulting cube:

enter image description here

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    I think you'll also need to say more about the flipping and rotating. If I flip a square and get a mirror image of its key/slot pattern, will that correspond to one of the other patterns? Also, if the squares can be joined perpendicularly and their patterns can be rotated and flipped, how do you decide which of them differ? This no longer seems to gel with the colour paradigm.2012-01-07

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Maybe I'm misunderstanding your problem, but it seems to me that you only need 2 colors to build a cube from 6 squares. If each square has top and bottom edges blue, left and right edges red, then you can fit 6 of them together to form a cube in such a way that wherever two squares meet, one has a blue edge, the other, red.

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    @joriki. Yes, that is what I've found as well. At the moment I have 8 colors. But as you said, it should be sufficient to have$4$colors. They should stack up nicely. Thank you for your help!2012-01-07