Willem wrote: ) clive tooth wrote: ) ) Let a P(n,s) be a continuous path, made of s straight sections, which ) ) passes exactly once through each of n^2 points arranged in a square ) ) array. ) ) ) ) So, here is a P(3,4)... ) ) http://www.flickr.com/photos/lhc_logs/8435448440/in/photostream ) ) ) ) I know of a P(4,6). But I cannot find a P(5,8). Any takers? ) ) IIRC, I figured out a way to get P(n,n*2-2) by beginning at P(4,6) in ) such a way that adding a row and column required two extra lines. ) ) I can't remember exactly what that beginning sequence was though.
Ah yes, now I remember. If you take the 3x3 solution you posted, the last line can be extended upward, and then you can draw lines right and down, adding a row and column to the top and right respectively. From there on you can keep on spiraling outward.
8-O-O-O-O-9 | | O 4-O-O-5 O | | | | O 1-O-O-2 O | |\ /| | O O O O O O | | X | | O O O # O O | |/ | | 7-3-O-O-6 10
SaSW, Willem -- Disclaimer: I am in no way responsible for any of the statements made in the above text. For all I know I might be drugged or something.. No I'm not paranoid. You all think I'm paranoid, don't you ! #EOT