Everyone19 Jan 2004

Here's a problem for you, Goad (though I daresay I only just invented it so it may be rife with schoolboy errors):

Assume an equilateral triangle shaped manhole cover, with sides of length x. Show that if we are to be sure the manhole cover CAN fall down the manhole, then its thickness must not exceed

(x/4)*(2*(root 3) - 3)

Indeed, if this result is correct, and we assume a reasonable value for x (say 1m?), then provided its thickness does not exceed about 11.6 cm, it WILL be able to fall down the manhole.

Is 11.6cm a spectacularly thick manhole cover? I daresay it is not, though more research in this field is DESPERATELY needed.

Good day to you, Sir!