Quandaries and Queries


You are working with a power saw and wish to cut a wooden cube 3-inches on aside into 27 1-inch cubes. You can do this by making six cuts through the cube keeping the pieces together in the cube shape. Can you reduce the number of necessary cuts by rearranging the pieces after each cut?



Unless I'm overlooking something, the answer is NO -- consider the middle cube. There must be a cut for each of its six faces.


In April 2012 Davis asked

Question from David:

If you assume the availablity of a second pair of hands
(who are prepared to risk some fingers),
can you not slice the cube in four cuts? Like this:

Standard first two cuts, then,
mark all the pieces for the next two standard cuts.
line up the pieces for the third cut, and
cutting slowly, as soon as the first is complete,
move the bigger piece needing what would have been a fourth cut
down to join the queue of pieces,
but with the fourth cut mark lined up with the third cut marks ahead of it.
ditto for second and third pieces.
Similarly, the fourth cut could be made to do the work of what
would have been the fifth and sixth standard cuts.
How about it?

Hi david,

Ingenious, but this rather redefines what we mean by a cut. If a piece can be run past the blade more than once within what is called "one cut," taking this to its logical extreme would suggest that the entire operation could be done in a single "cut", with pieces put back into the queue several times.

But what we would then be counting would be more clearly referred to as "times we turn the saw on" or something like that.

Good Hunting!


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