The is a large cube formed by gluing together 27 smaller cubes of uniform size (see figure). A termite starts at the center of a face of any of the outside cubes and bores a path that takes him once through each cube. His movement is always parallel to a side of the large cube, never diagonal.
Is it possible for the termite to bore through each of the 26 outside cubes once and only once, then complete his journey by entering the central cube for the first time?
If possible, show how; if not, prove it.
This puzzle is from Martin Garner's The Colossal Book of Short Puzzles and Problems.
I hope the problem is not too boring (ahem) for members of this forum.