Consider a wooden 5x5x5 block. A termite wishes to eat the block in the following way

1) It starts with an external, central 1x1x1 cube of any face.
2) The termite eats it, and the heads towards a neighboring 1x1x1 cube.
3) It repeats step 2 until it can't go any further.

Determine:

a) A possible path for the termite to follow, in order to eat every single 1x1x1 cube.

b) If it's possible for the termite to eat all 1x1x1 cubes, knowing it ate the central internal cube last.

If he were to follow the edges, around all corners of the cube, not only would he have a specific path, but it would enable him to consume the center last.

Posted by Gt Vegita on 2003-07-06 21:02:26