Let S be a square with sides length 100. X and Y of L such that the distance between X and Y is not greater than 1 and the length of the part of L which lies between X and Y is not smaller than 198.
Solution Let the square be A'B'C'D'.
The idea is to find points of L close to a particular point of A'D' but either side of an excursion to B'. Let A' be the first vertex of the square approached by L. L must subsequently approach both B' and D'. Suppose it approaches B' first. Take X' to be the point on A'D' closest to D' which is approached by L 1 . Let X be the corresponding point on L 1 .