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.
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."