18-Point Problem
Place a point somewhere on a Line Segment. Now place a second point and number it 2 so that each of the points is in a different half of the Line Segment. Continue, placing every 
th point so that all points are on different 
th of the Line Segment. Formally, for a given , does there exist a sequence ofreal numbers 
, 
, ..., 
such that for every 
and every 
, theinequality
holds for some
? Surprisingly, it is only possible to place 17 points in this manner(Berlekamp and Graham 1970, Warmus 1976).Steinhaus (1979) gives a 14-point solution (0.06, 0.55, 0.77, 0.39, 0.96, 0.28, 0.64, 0.13, 0.88, 0.48, 0.19,0.71, 0.35, 0.82), and Warmus (1976) gives the 17-point solution
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References
Berlekamp, E. R. and Graham, R. L. ``Irregularities in the Distributions of Finite Sequences.'' J. Number Th. 2, 152-161, 1970. Gardner, M. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications. New York: Springer-Verlag, pp. 34-36, 1997. Steinhaus, H. ``Distribution on Numbers'' and ``Generalization.'' Problems 6 and 7 in One Hundred Problems in Elementary Mathematics. New York: Dover, pp. 12-13, 1979. Warmus, M. ``A Supplementary Note on the Irregularities of Distributions.'' J. Number Th. 8, 260-263, 1976.
- 239
- 24-Cell
- 257-gon
- 2x mod 1 Map
- 3
- 3x+1 Mapping
- 42
- 600-Cell
- 65537-gon
- 666
- 72 Rule
- AAA Theorem
- AAS Theorem
- Abacus
- abc Conjecture
- Abelian
- Abelian Category
- Abelian Differential
- Abelian Function
- Abelian Group
- Abelian Integral
- Abelian Variety
- Abel's Curve Theorem
- Abel's Functional Equation
- Abel's Identity