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.
(In reply to
re: Reminds me of Konigsberg Puzzle by TomM)
Actually I misread the opening '5x5x5 block' stipulation; that would be painful to follow through with that may pathes!
But playing with a 3x3 model, using the ask of the author's 1a)stipulation, I can get the termite to finish at the centre cube of the opposite face.
Question: Can I assume with a solution for this 3x3 case that a 5x5 automatically follows?
Back to Konigsberg. How would a collary read? Could it be used to prove or disprove the b) possibility? I cannot perceive a solution from a centre faced cube of my model, but then I haven't started at a 'vertex' or 'centre of edge'.
re(2): Reminds me of Konigsberg Puzzle
