Solved cryptogram
A solid ball can in principle be cut into pieces and rebuilt as two balls of the same size.
Mathematics Facts, sourced to Wolfram MathWorld.
Solve it yourself
This fact is a cryptogram here: 72 letters over 19 different ones, graded medium.
Or go to the puzzle’s own page first.
What it means
This is a real theorem and not a trick, and the catch is in the word pieces. They are not solids you could cut with a knife; they are scattered clouds of points with no sensible volume at all, so no volume gets doubled because none of the parts had one. Producing them requires the axiom of choice, which is why the result is often quoted as evidence of how strange that axiom is rather than as a fact about balls.
The claim comes from Wolfram MathWorld.
- SourceWolfram MathWorld
- CollectionMathematics Facts
- Difficultymedium
- Length72 letters, 19 of them different
Nearby in the collection
The facts either side of this one.
- MacTutor History of Mathematicsmedium, 71 letters
- Wolfram MathWorldmedium, 80 letters
- Wolfram MathWorldmedium, 74 letters
- Wolfram MathWorldmedium, 75 letters
About as hard as this one
Scored closest to it by the model behind our guide to solving cryptograms.
- MacTutor History of Mathematicsmedium, 72 letters
- Wolfram MathWorldmedium, 75 letters
- Wolfram MathWorldmedium, 72 letters
- Wolfram MathWorldmedium, 68 letters