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A star of n (n greater than or equal to 2) line segments (needles) of equallength with common endpoint and constant angular spacing is randomly placedonto a lattice which is the union of two families of equidistant lines in theplane with angle alpha between the nonparallel lines. For odd n, we calculatethe probabilities of exactly i intersections between the star and the lattice(for even n, see [3]). Using a geometrical method, we derive the limitdistribution function of the relative number of intersections as n tends toinfinity. This function is independent of alpha. We show that the relativenumbers for each of the two families are asymptotically independent randomvariables.

Buffon's problem with a star of needles and a lattice of parallelograms