Can a postman walk every street once and get home without backtracking?
Imagine a mail carrier who must walk every street in a neighbourhood at least once and return to the post office, covering as little repeated ground as possible. If every street corner has an even number of streets meeting at it, the postman can walk the whole route without ever retracing a single step. What happens if some corners have an odd number of streets instead?
Reveal the answer
The postman has to retrace some streets — specifically, the shortest route requires re-walking just enough streets to make every corner's count even again, which can be found by pairing up the odd corners as cheaply as possible. Chinese mathematician Guan Meigu first solved this problem in a 1960 paper, translated into English in 1962; the route is unusual among optimisation puzzles for being solvable quickly, unlike its harder cousin, the travelling salesman problem.