just another interesting problem.

[Gurel-gurevitch Ori]

This is another problem I saw many years ago, I hope you'll enjoy it.
1)
given a cube you want to cut it into 27 equale smaller cube. you can
do this easely with 6 cuts, 2 for each axis. now lets assume you are
allowed to move the pieces after each cut, this means that after the
first cut you can put one of the parts on the other and to cut them
both together. the question is with this method, how many cuts are
needed to cut the cube into 27 parts?
2)
the same question just that now there is a hypercube and you want to
cut it into smaller hypercubes.the hypercube has n dimentions and you
want to cut the first side into a1 parts the second a2 etc the n-th

part an so that you'll have a1*a2*...*an hyper cubes at the end.

The first question is of course a simple case of the second one where
n=3 and a1=a2=a3=3.goodluck,
J.

--

Gurel-Gurevitch Ori jhus...@libra.math.tau.ac.il