The Two Corners Claim:Seen from the top, as the path moves on the walls it always passes exactly two corners. Proof: It must pass at least one corner, since {$c>a,b$}. It can't pass three because {$c\le a+b$}. But if it ever passed just one corner,  then by symmetry it would have earlier passed by just one corner  (note that on the left {$p+c+q=a+b$}, and on the right, {$p+c+r=a+b$}, so {$q=r$}). Thus there can't be a first time to pass just one corner. |