rsl12

PS. if the pieces don't rotate, you can try a multi-color scheme. Here's a 3-color scheme:

ABC
CAB
BCA

Each shape then gets a three values associated with it:

1,1,1
1,1,1
2,0,2
2,1,1
2,2,2
1,0,0
1,1,0
2,0,2

In this case the constraints are X mod 2 = 1, Y mod 2 = 1, and Z mod 2 = 1 (you need only check 2 of the 3 however).

You can convince yourself that you can 'flip' (or rather, 'rotate') the numbers in any of 3 possible combinations. If you had something that was

1,2,3

you could rotate the values (not the shape) so that it was

2,3,1
3,1,2

but flipping two numbers doesn't work:

1,3,2 would be a different shape (or you would have rotated the shape).

In choosing a color scheme, the trick seems to be to get as few numbers that give you the same result when you mod them. [For example, (2,0,4) mod 2 is (0,0,0), and (1,1,1) mod 2 is (1,1,1). You aren't optimizing anything associated with these two guys.] The 3-color scheme, in this case, seems to give you no benefit over the 2-color one (though I could be wrong).

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