Question 119
In a wooden block shaped like a cube, all the vertices and edge midpoints are marked. The cube is cut along all possible planes that pass through at least four marked points. Let $N$ be the number of pieces the cube is cut into. Estimate $N$.
An estimate of $E \gt 0$ earns $\lfloor 20 \min (N / E, E / N)\rfloor$ points.
An estimate of $E \gt 0$ earns $\lfloor 20 \min (N / E, E / N)\rfloor$ points.