i have been given a puzzle cube (4x4x4) which is meant to be composed from various differently shaped pieces of mainly five units each, similar to tetris shapes. I was wondering if there is a better way than trial and error of making the larger cube. Also, i was wondering if there was more than one way of doing it, other than the various rotations of the same solution.
2006-10-02 06:58:19 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
sorry, i wasn't clear enough. I have an actual puzzle already, composed of 5 unit blocks which are all different. There is also a 4x4x4 perspex cube into which they will all fit. ( yes one is 4 units, but all the others are five )
I have grown tired of randomly fitting the pieces together without any stategy and was wondering how i could go about it more efficiently.
2006-10-03 04:04:43 · update #1
you should use lagrangian interpolation and remove the non linear subsets.
2006-10-06 05:57:34 · answer #1 · answered by ebayphonehome 2 · 0⤊ 1⤋
There are numerous ways to split a 4x4x4 cube into smaller units. First realize, that 4x4x4 = 64, so you can't make it all of 5 unit pieces. At a minimum, one will have to be a 4 unit piece.
Other than that, I think trial and error is a fine way to do it. You can do it as layers on paper, or build an actual model. There is no single "right" answer. In fact, it isn't that hard to come up with one. The only hard part would be if there are other restrictions, such as not being able to repeat a 5-unit shape, for example.
2006-10-02 07:18:05 · answer #2 · answered by Puzzling 7 · 0⤊ 0⤋
How about 5 4x4 quadratic based slabs of 4/5th height? Fairly simple to make too.
2006-10-02 07:14:09 · answer #3 · answered by Anonymous · 0⤊ 0⤋
I wouldn't have thought there were any strategies especially different from 2D, start with corners, then edges, then the middle ones.
2006-10-02 10:26:35 · answer #4 · answered by THJE 3 · 0⤊ 0⤋