SUMMARY
In 30 seconds
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.
Takeaways
- 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.
FULL TEXT
Read the edited text by chapter
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.
More from this channel
40:44EN
3Blue1Brown· Oct 16, 2026Grant Sanderson: There's never been a better time to go into mathGrant Sanderson, Constantin Kogler · 3Blue1BrownStudents fear AI has solved mathematics. Grant Sanderson argues the opposite: even if machines prove theorems better than we do, the institution of math stays valuable—and this is a rare moment when newcomers can reshape it.
51:55EN3Blue1Brown· Sep 18, 2026The last IMO problem AI could not solveGrant Sanderson · 3Blue1BrownGrant Sanderson walks through IMO 2025 Problem 6 — a tiling puzzle that frontier models missed — and the visual patience it takes to prove a construction is optimal.
2:25EN3Blue1Brown· Jun 12, 2026How Shannon Measured the Entropy of EnglishA guessing game helped Claude Shannon estimate how much information English text contains, and why prediction is central to compression.
1:02EN3Blue1Brown· Jun 10, 2026A Robot Walk and the Puzzle of Optimal Binary EncodingHow few bits does it take to send directions that occur with unequal frequencies?
32:19EN3Blue1Brown· Jun 7, 2026Reinventing Entropy: Why Prediction Helps Compress LanguageA robot’s movement code leads from prefix-free encoding to Shannon information and the entropy of language.
0:48EN3Blue1Brown· Mar 25, 2026The Subset Sum Puzzle: Who Has a Winning Strategy?Choose ten integers from 1 to 100, then look for two different subsets with the same sum.