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Solving Soma cube (Updated with images/pieces)
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Updated the original post with a quick image of all the pieces. Its a bit shaky but i exagerated the proportions to try and make it obvious which are half pieces and which are whole cubes.
A cookie to anyone who can solve it
A cookie to anyone who can solve it
quote:Original post by OrangyTangI would think this would make the search easier, since there are only so many places each piece can go. Also, when you have a half black cube, only another half black cube can fit in the empty space to fill the rest of the cube - this limits the number of pieces that can be chosen to be put there. Perhaps using a 3x3x3 array would be easier (at least in the theory of the solution). What do you think?
Also, each cube is either white or black, and the final solution is supposed to be checkered on every side.
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More progress I entered the Soma pieces as an easier test of the algorithm, and if i hardcode the first piece to a position i know has a solution (just to trim the tree a little) it finds a solution within about a minute. I''ve reworked it so it actually plays nice with other apps as well. The Soma cube is much simpler and has less pieces though..
Left it solving the full bastard-cube set when i went to work, got back after it had been running all day and no solution found
I think i''m going to add colour checking, as it was trying pieces that were obviously wrong to me, yet the program is blind to it. Adding colour checking should also have a side effect of aligning the pieces to the 3x3x3 grid properly
Colour checking is hopefully none too difficult, i also have one more piece of information to go on - the pieces have one more black cube than white cubes, therefore the corners of the solution have to be black. I''m still going to stick with the 3x3x3 grid, it makes dealing with the half pieces easier, as i don''t have to write a bunch of special case code everywhere.
Oh, i''m also tempted to add Timkin''s suggestions to remove duplicate rotation/translation combinations, but since the algorithm probably works in its current state i''m tempted to leave it alone. Then again, i''d also like the results to be calculated in my lifetime
I entered the Soma pieces as an easier test of the algorithm, and if i hardcode the first piece to a position i know has a solution (just to trim the tree a little) it finds a solution within about a minute. I''ve reworked it so it actually plays nice with other apps as well. The Soma cube is much simpler and has less pieces though..Left it solving the full bastard-cube set when i went to work, got back after it had been running all day and no solution found
I think i''m going to add colour checking, as it was trying pieces that were obviously wrong to me, yet the program is blind to it. Adding colour checking should also have a side effect of aligning the pieces to the 3x3x3 grid properly Colour checking is hopefully none too difficult, i also have one more piece of information to go on - the pieces have one more black cube than white cubes, therefore the corners of the solution have to be black. I''m still going to stick with the 3x3x3 grid, it makes dealing with the half pieces easier, as i don''t have to write a bunch of special case code everywhere.
Oh, i''m also tempted to add Timkin''s suggestions to remove duplicate rotation/translation combinations, but since the algorithm probably works in its current state i''m tempted to leave it alone. Then again, i''d also like the results to be calculated in my lifetime
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