Irregularity_of_distributions
The irregularity of distributions problem, stated first by Hugo Steinhaus, is a numerical problem with a surprising result. The problem is to find N numbers, , all between 0 and 1, for which the following conditions hold:
- The first two numbers must be in different halves (one less than 1/2, one greater than 1/2).
- The first 3 numbers must be in different thirds (one less than 1/3, one between 1/3 and 2/3, one greater than 2/3).
- The first 4 numbers must be in different fourths.
- The first 5 numbers must be in different fifths.
- etc.
Mathematically, we are looking for a sequence of real numbers
such that for every n ∈ {1, ..., N} and every k ∈ {1, ..., n} there is some i ∈ {1, ..., k} such that