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 . The number 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 A014552 in ``The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.

© 1996-9

1999-05-26