263. On a plane, several non-intersecting segments are given, no two of which lie on the same line. We want to draw several more segments connecting the ends of the given segments so that all segments together form one non-self-intersecting broken line. Is it always possible to do this?
263. Answer: not always.

Fig. 107 shows an example of 6 segments - 3 short and 3 long, which cannot be included in a non-self-intersecting (even open) broken line in the required manner. Indeed, one of the short segments is not at the end of the broken line, but its ends can be connected by lines to the ends of the nearby long segment.