The Problem of the Thrown String
John Lighton Synge · The Mathematical Gazette · 1970
Some time ago I asked what is the average rectilinear distance D between the ends of a string of length L when thrown down at random on a table (The Mathematical Gazette , LII (1968) 165). I have to thank a number of correspondents (J. Clemow, R. 0. Davies, A. R. Everett, M. Fine, J. R. Hunt, G. S. Light and E. Sike) for letters about the problem. Some offered solutions based on simple assumptions regarding randomness. The simplest (Everett) is that all values of D in the range (0, L) are equally probable, and so the answer is \L . I do not find this assumption acceptable, nor the other assumptions put forward.