The 64 sugar cubes puzzle — Transcript
Full transcript
- 0:00It's time for a new puzzle of the month.
- 0:02This one comes from a problem on the 2024 British Math Olympiad.
- 0:06The setup is to have 64 sugar cubes arranged in a 4x4x4 block.
- 0:11Each cube is either white, blue, or brown.
- 0:14Your challenge is to prove that you can find 6 pairs of cubes,
- 0:18such that all 12 individual cubes involved are the same color,
- 0:21and such that the lengths of these six lines,
- 0:24the lines connecting the centers of the cubes in a given pair, are all the same.
- 0:28And that's 6 equal distances.
- 0:31So just to be clear, you have to show that no matter what the allocation of colors
- 0:36to these 64 different spots in our big 4x4x4 cube is, you can always do this.
- 0:41You can always find 12 little cubes of the same color that can be divided into 6
- 0:45different pairs such that there's a common distance between the centers of each pair.
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