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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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    Please consider that the squares (tiles) can be flipped which results in a mirrored "key-and-slot-pattern". They also can be rotated.2012-01-07
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    I thought I understood what you're saying but the sentence "That way each square has $x$ colors whose edges can be joined to each other as long as their color differentiates." threw me off. It seems to refer to colors of edges of colors. Did you mean "That way each square has $x$ colors and the edges of the squares can be joined to each other as long as their color differs"? Also, how should we interpret "I have squares whose $4$ edges have $x$ different key-and-slot-patterns." and "each square has $x$ colors"? Is it the edges or the squares that have $x$ colours each?2012-01-07
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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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