[jyl]

Here is a question someone posed to me. I do not know the answer, but thought I'd give you guys equal opportunity to be frustrated.

There is a square, centered on the origin. At each corner of the square is a spider. The spiders are "D" distance apart. Each spider will always crawl directly toward the next spider, "next" meaning counterclockwise, wherever that next spider is located at that instant. All spiders crawl at the same speed "S", and all start crawling at the same time. Will any spider ever reach the origin? If yes, how far will he crawl to get there?

I am told there is a messy way to solve this (calculus), and at least two simple/elegant ways.