A wooden cube is to be sawn into 27 identical small cubes. Between one cut and the next the pieces may be moved about and stacked in any way you please, and each cut is a single straight stroke of the saw. What is the smallest number of cuts that will do it?

Six cuts plainly work — two cuts in each of the three directions — so the question is whether clever stacking can do better. It cannot. Think of the little cube that finishes in the very middle of the big one: none of its six faces is part of the original outside surface, so each of those six faces has to be created by a saw stroke, and one straight stroke cannot make two faces of the same little cube. So at least 6 cuts are needed, and stacking saves nothing at all. The traps: 4 is the hope that stacking pieces on top of one another will cut the work down; 9 counts three cuts in each direction instead of two; 8 is the number of pieces a cube falls into after three cuts, a count of pieces mistaken for a count of cuts.