Given
matches (i.e., rigid unit line segments), find the number of topologically distinct
planar arrangements which can be made (Gardner 1991). In this problem, two matches
laid end-to-end with no third match at their meeting point are considered equivalent
to a single match, so triangles are equivalent to squares, -match tails are equivalent to 1-match tails, etc.
Solutions to the match problem are planartopological graphs on
edges, and the first few values for , 1, 3, 5, 10, 19, 39, ... (OEIS A003055).
Gardner, M. "The Problem of the Six Matches." In The
Unexpected Hanging and Other Mathematical Diversions. Chicago, IL: Chicago
University Press, pp. 79-81, 1991.Read, R. C. "From Forests
to Matches." J. Recr. Math.1, 60-172, Jul. 1968.Sloane,
N. J. A. Sequence A003055/M2464
in "The On-Line Encyclopedia of Integer Sequences."
matches (i.e., rigid unit line segments), find the number of topologically distinct
planar arrangements which can be made (Gardner 1991). In this problem, two matches
laid end-to-end with no third match at their meeting point are considered equivalent
to a single match, so triangles are equivalent to squares, 
-match tails are equivalent to 1-match tails, etc.
edges, and the first few values for 
, 1, 3, 5, 10, 19, 39, ... (OEIS A003055).
