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 the work ate the first face by spiraling out, then eating down one square, then eating the rows of the next layer back and forth, crossing the layer and ending at an opposite corner. The worm could eat down one again and then eat a spiral around the third layer, also the original center layer, not eating the very center cube, instead stoppiong on one adjacent to it, eat down again, eat in a spiral fashion that did the revers of the previous layer, ending him at the corner of the layer, down one, a full spiral inside to the center, eat up the last to cubes straight up and end at the center cube in the center layer.

Posted by Jon on 2003-05-09 06:49:02