HMMT February, 2018

Geometry Difficulty 4.7 AIME Find the answer United States

Problem:

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 $E>0$ earns $\lfloor 20 \min (N / E, E / N)\rfloor$ points.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:

15600

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.