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.
Won't reflect on Konigsberg (2 islands in river and 6 bridges, I think; islands are linked to each other, and each to each bank, and then the last bridge spans the river). The network of this scenario cannot be traced back to point 'X' without covering previous ground.
Let us convert the termite's cube into 27 connected locations within a plane. Hey, it's messy, but it can be done. From there look at the two aspects of the problem as posed.