Langford's Problem

Arrange copies of the digits 1, ..., such that there is one digit between the 1s, two digits between the 2s, etc. For example, the solution is 312132 and the solution is 41312432. Solutions exist only if . Thenumber of solutions for , 4, 5, ... are 1, 1, 0, 0, 26, 150, 0, 0, 17792, 108144, ... (Sloane's A014552).

References

Gardner, M. Mathematical Magic Show: More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleight-of-Mind from Scientific American. New York: Vintage, pp. 70 and 77-78, 1978.

Sloane, N. J. A. Sequence A014552in ``The On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.

• Heat Conduction Equation--Disk
• Heaviside Calculus
• Heaviside Step Function
• Heawood Conjecture
• Hebesphenomegacorona
• Hecke Algebra
• Hecke L-Function
• Hecke Operator
• Hecke Ring
• Hectogon
• Hedgehog
• Heegaard Diagram
• Heegaard Splitting
• Heegner Number
• Heesch Number
• Heesch's Problem
• Height
• Heilbronn Triangle Problem
• Heine-Borel Theorem
• Heine Hypergeometric Series
• Heisenberg Group
• Heisenberg Space
• Held Group
• Helen of Geometers
• Helicoid