Solved cryptogram
Give a strip of paper a half twist and tape the ends, and the loop you get has only one side.
Mathematics Facts, sourced to Wolfram MathWorld.
What it means
Run a pencil along the surface without lifting it and you return to where you started having covered what looks like both faces. It has one edge too. Cutting it down the middle does not give you two loops; it gives one longer loop with a couple of twists in it. The shape is a standard first example of a surface that cannot be consistently assigned an inside and an outside.
The claim comes from Wolfram MathWorld, and the page it comes from was read on 2026-08-27 to confirm it still says this.
This is not the kind of claim that goes out of date, which is why it was set as a puzzle rather than a fact with a shelf life.
Solve it yourself
This fact is a cryptogram here: 71 letters over 18 different ones, graded easy.
- SourceWolfram MathWorld
- CollectionMathematics Facts
- Difficultyeasy
- Length71 letters, 18 of them different
Nearby in the collection
The facts either side of this one.
- Wolfram MathWorldhard, 79 letters
- Wolfram MathWorldmedium, 74 letters
- Wolfram MathWorldmedium, 70 letters
- Wolfram MathWorldeasy, 77 letters
About as hard as this one
Scored closest to it by the model behind our guide to solving cryptograms.
- Wolfram MathWorldmedium, 77 letters
- Wolfram MathWorldmedium, 76 letters
- Wolfram MathWorldmedium, 75 letters
- Wolfram MathWorldmedium, 79 letters