The football / string one is quite cool, I worked out something similar one day purely out of boredom, sat in roadworks on the M25.
I thought, i wonder how much further it is to circuit the M25 in the inside lane of the clockwise carriageway (the outer one) compared to the inside lane of the anti-cw one, thinking that on a ‘circle’ that big it might be some distance.
So approximating it as a circle, I estimated the difference in radius to be maybe 20m. So, circumference of inner = pi x diam of inner; circumference of outer = pi x (diam+40) Cancel out and you’re left with the difference as pi x 40 = about 125m.
So my quiz question would be: if Usain Bolt cloned and then raced himself around the m25, one in the inner lane, one in the outer, how much headstart should he allow to make it a decent race?