A 3x3x3 cube of cheese can be cut into 27 1x1x1 cubes with 6 cuts (2 along every dimension; like a Rubik's Cube).

geometry/cube.cuts New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

A 3x3x3 cube of cheese can be cut into 27 1x1x1 cubes with 6 cuts (2
along every dimension; like a Rubik's Cube).  Can a 3x3x3 cube be cut
into 27 1x1x1 cubes with LESS than 6 cuts?  If so, how?  If not, why
not?

Only straight cuts are allowed.  After a cut has been made, the
resulting pieces may be moved around and stacked up, before the next
cut.

-- Julian <julian@cs.uq.oz.au>

Show solution

Consider the small cube at the center of the 3x3x3 cube.  All six of
its faces must be cut in order to form the small cube.  No matter how
you stack the pieces, it is impossible to cut more than one of the
faces of the small center cube with a single cut.

This puzzle has been mentioned by Martin Gardner.  I don't have a
reference right now -- sorry.

-- Dave Seaman <ags@seaman.cc.purdue.edu>