tag:blogger.com,1999:blog-2705471569279322484.post150366636490174737..comments2023-08-25T19:28:22.200+08:00Comments on etcetera: screw mathematical models. bread is where it's at.etchttp://www.blogger.com/profile/13427342295118039486noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-2705471569279322484.post-71121504598752754362009-09-11T09:39:52.952+08:002009-09-11T09:39:52.952+08:00for those interested:
you can show that for a squ...for those interested:<br /><br />you can show that for a square of roads n by n, the number of possible routes without backtracking is :<br /><br />Sn = n(n+1)<br /><br />(you can prove this by induction, if you want).<br /><br />use this as a template for modified squares, by subtracting roads (alternatively add roads, but subtracting is less work):<br /><br /> {S'(m0)<br />Sn = n(n+1) - {S'(m0) + ... + S'(mj)<br /> {S'(p)<br /><br />need to find a way to actually write in formulae, because it's effin hard to describe this without being able to write it up properly. <br /><br />anyway give the formula a try and you'll probably see what i mean.<br /><br />some additional info that might help, for a square m by n, you can use the same derivation, but you'll end up with something similar to the middle term of the formula above.<br /><br />happy calculating!etchttps://www.blogger.com/profile/13427342295118039486noreply@blogger.com