I saw this brain teaser.
Suppose, we travel 1000 miles on a tricycle and we have 5 tyres, then how many times do we need to stop to change tyres so that each of the tyres travelled the same distance?
Here is a solution: After 400 miles change the back two tyres (could be any two) * After 600 miles change the front tyre for one of the ones that has 400 miles * After 800 miles change the front tyre again for the remaining tyre that has 400 miles.
So the answer is 3 stops, 4 changes.
However, suppose, if we have $M$ for an $N$-cycle, then what is the minimum number of changes and number of stops? It is not clear to me that there is a straightforward formula for stops. I imagine there is one for number of changes.