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3Blue1Brown poses a puzzle based on a 2024 British Mathematical Olympiad problem, leaving its proof to the reader.
- 1Arrange 64 sugar cubes in a 4×4×4 block. Each cube is white, blue or brown.Arrange 64 sugar cubes in a 4×4×4 block. Each cube is white, blue or brown.
- 2Prove that there are six pairs containing 12 distinct cubes, all of one colProve that there are six pairs containing 12 distinct cubes, all of one color, such that the distance between the centers of each pair is the same.
- 3The proof must work no matter how the three colors are assigned to the 64 pThe proof must work no matter how the three colors are assigned to the 64 positions. The short video poses the challenge without giving the solution.
Das Wichtigste
- Arrange 64 sugar cubes in a 4×4×4 block. Each cube is white, blue or brown.
- Prove that there are six pairs containing 12 distinct cubes, all of one color, such that the distance between the centers of each pair is the same.
- The proof must work no matter how the three colors are assigned to the 64 positions. The short video poses the challenge without giving the solution.
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01
The question
Arrange 64 sugar cubes in a 4×4×4 block. Each cube is white, blue or brown.
Arrange 64 sugar cubes in a 4×4×4 block. Each cube is white, blue or brown.
02
The implications
The proof must work no matter how the three colors are assigned to the 64 positions. The short video poses the challenge without giving the solution.
Prove that there are six pairs containing 12 distinct cubes, all of one color, such that the distance between the centers of each pair is the same.
The proof must work no matter how the three colors are assigned to the 64 positions. The short video poses the challenge without giving the solution.
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