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This rubics cube would consist of LEDs in the appropriate
colors and locations. It would have an accelerometer to
determine "down". When it's close to being solved the
colors would change just on the bottom (where the user
least likely to be looking) in appropriate patterns. As the
turns it, the faces turned toward the bottom would
also be changed such that it would always require just
three more turns to finish.
The trick feature could be turned off.
Bonus 2: autocomplete
Bonus 3: auto half complete
Bonus 4: puzzle sets
Bonus 5: changing pictures, faces, and patterns
Bonus 6: music and light display when it's completed to
reward the user
||If you're only swapping colours on the bottom face then it would presumably be possible to beat by solving one face and then turning that to the bottom.
||I wonder whether it's possible to design a (passive) apparently syntactically correct Rubik's cube which can't be solved. Of course you can create something which would pass rudimentary inspection by arranging, say, for edges and/or vertex cubes to show combinations of all six colours. This is easy, by swapping coloured stickers between the component cubes.
But I suppose that if you effectively take a Rubik's cube to bits and reassemble it -without moving coloured stickers around - you might be able to create a much more subtle issue which would prevent the cube from being solved.
<edit>The Wikipedia Rubik's cube article states that there are 12 distinguishable configurations of the cube, but these differ only by swapping a single pair of pieces or rotate a single corner or edge cube. It would be relatively easy to determine a trick cube by near-solving and identifying the swapped pieces or rotated piece. Which means that an active method would be necessary.
||Not long after I first got a rubik's cube I disassembled it and put it together again (randomly) only to realise I could no longer solve it.
||Never quite understood the obsession with peeling the stickers off when you can take them apart so much easier.
||Maybe a passive cube which allows a non-standard rotation easily would catch people out? If you could solve it in front to them, but then slyly rotate a corner when you scramble it, it might work.