keesan@bbncca.ARPA (Morris Keesan) (11/30/83)
------------------------------- I'm amazed at the number of people who have apparently gone ahead and posted their solutions without first checking them. The most common error seems to be the one in the "solution" just posted by Andrew Glassner, wherein people seem unaccountably blind to the fact that the center horizontal line has FOUR segments, not three: +---------+---------------+-------+ | | | | +----1----+---2---+---3---+---4---+ | | | +-----------------+---------------+ Before anyone posts any more "simple" solutions, make sure your line touches both segments 2 and 3. As several people have pointed out, the Euler's results from the Konigsburg bridges problem rule out any of the obvious/simple solutions. I believe the key to this problem lies in the interpretation of the phrase "pass through a line." If you interpret this to mean "intersect the line at a point", the problem is insoluble. This is a little hard to draw on a terminal, but the key "aha" is to realize that a curve can "pass through" a line segment by coinciding with it for its entire length. If one imagines the line segment to have a thickness, it's easier to draw. The "edges" of the line segment are represented below by hyphens (-), and the line "passing through" by '>'s. ----------------------- >>>>>>>>>>>>>>>>>>>>>>> ----------------------- If this is allowed, the problem becomes truly simple, by "passing through" any one of the internal vertical line segments in this way. This is roughly equivalent to swimming the length of one of the Konigsburg canals.