In 30 seconds
3Blue1Brown asks how many distinct frames can be made by removing edges from a cube when rotations count as the same configuration. The short connects the question to Sol LeWitt’s 1974 artwork and introduces a longer guest video by Paul Dancstep; it does not give the count.
- 1Remove edgesThe puzzle counts partial cube frames made by leaving out edges.
- 2Account for rotationsConfigurations related by a rotation are considered identical.
- 3Art and group theoryA related constrained problem inspired a 1974 Sol LeWitt artwork and leads toward Burnside’s lemma.
Takeaways
- Removing edges from a cube produces many partial frames.
- Two frames count as the same when one can be rotated to match the other.
- The related artwork has additional constraints, and the longer video explores Burnside’s lemma.
Read the edited text by chapter
The incomplete-cube puzzle
Remove cube edges and count distinct frames, identifying those that differ only by rotation.
How many ways can a cube be incomplete? Take a cube’s edge frame and remove some edges. The question is how many distinct partial frames can be made.
There is a catch: if you can rotate one incomplete cube to match another, they count as the same configuration. Simply counting every choice of edges would therefore count some arrangements more than once.
Art and a mathematical method
The presenter relates the question to Sol LeWitt’s work and a longer video exploring group theory.
With additional constraints, a related question formed the premise of a 1974 artwork by Sol LeWitt. The short points to a longer guest video by Paul Dancstep, which tells the artwork’s story alongside a problem-solving process leading to group theory and Burnside’s lemma. This short invites viewers to think about the puzzle without giving the count.
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