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.

• Direction Cosine
• Directly Similar
• Director Curve
• Direct Product (Group)
• Direct Product (Matrix)
• Direct Product (Set)
• Direct Product (Tensor)
• Directrix (Conic Section)
• Directrix (Graph)
• Directrix (Ruled Surface)
• Direct Search Factorization
• Direct Sum (Module)
• Dirichlet Beta Function
• Dirichlet Boundary Conditions
• Dirichlet Conditions
• Dirichlet Divisor Problem
• Dirichlet Energy
• Dirichlet Eta Function
• Dirichlet Fourier Series Conditions
• Dirichlet Function
• Dirichlet Integrals
• Dirichlet Kernel
• Dirichlet Lambda Function
• Dirichlet L-Series
• Dirichlet Region