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Omni-MATH / In a wooden block shaped like a cube, all the vertices and edge midpoints are…

Problem

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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 NN be the number of pieces the cube is cut into. Estimate NN. An estimate of E>0E>0 earns ⌊20min(N/E,E/N)⌋\lfloor 20 \min (N / E, E / N)\rfloor points.
Plain-text mathematical notation (without MathML)
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 ⌊20min(N/E,E/N)⌋ points.
Original LaTeX notation
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.

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Source and history

task_id
5035af5b-46c0-5114-bc90-195547447587
task_key
test--5035af5b-46c0-5114-bc90-195547447587
task_revision_id
1
config / split
/ test

Official source

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