A while back I did a post about counterintuitive math problems. However, I deliberately held one back, since I was using it as my Problem of the Week for that week. So here it is:

Suppose a steel beam, one mile long, is fastened securely to the ground at each end. As the

day heats up, the metal expands. Let us assume that at the hottest part of the day, the metal

is actually one mile and one foot long. Let us further assume that the beam is fastened in such

a way that it can only buckle upward, and not side to side. Your problem is to estimate how

high the beam will rise above the ground. Would you be able to slip a playing card under it?

A pencil? Would you be able to crawl under it? Walk under it? Could an elephant (roughly

13 ft tall) walk under it? How about a person standing on the back of an elephant? That sort

of thing. Be sure to justify your answer!

Keep in mind I’m only asking for an approximation here, so feel free to help yourself to whatever (reasonable) simplifying assumptions you want. Or you can just follow the link above. This one was Problem Nine.