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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

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