Solved cryptogram
A hotel with an endless corridor of full rooms can still take a new guest without evictions.
Mathematics Facts, sourced to Wolfram MathWorld.
Solve it yourself
This fact is a cryptogram here: 75 letters over 19 different ones, graded medium.
Or go to the puzzle’s own page first.
What it means
Ask everyone to move up one room. The guest in room one goes to room two, room two to three, and so on. Nobody is left standing, because every room has a next one, and room one is now empty. The same trick with even numbers seats a whole busload of new arrivals. Hilbert used the story to make one point: for infinite collections, being full and having room are not opposites, which is where ordinary counting stops applying.
The claim comes from Wolfram MathWorld.
- SourceWolfram MathWorld
- CollectionMathematics Facts
- Difficultymedium
- Length75 letters, 19 of them different
Nearby in the collection
The facts either side of this one.
- Wolfram MathWorldmedium, 72 letters
- Wolfram MathWorldmedium, 74 letters
- Wolfram MathWorldhard, 72 letters
- Wolfram MathWorldeasy, 70 letters
About as hard as this one
Scored closest to it by the model behind our guide to solving cryptograms.
- Wolfram MathWorldmedium, 76 letters
- MacTutor History of Mathematicsmedium, 71 letters
- Wolfram MathWorldmedium, 71 letters
- Wolfram MathWorldmedium, 77 letters