Solution
The Fly and the Trains
Show the problem again
Two trains 100 miles apart head toward each other, each traveling at 50 mph. A fly leaves one train at 75 mph, flies to the other, turns around instantly, and repeats until the trains meet. What total distance, in miles, does the fly travel?
Worked solution
The answer is 75 miles. The trains close at 100 mph, meeting in exactly 1 hour. The fly flies at 75 mph for that entire hour, so it covers 75 miles. The trap is attempting to sum the infinite series of legs, which works, but the time-based shortcut makes it a one-liner. (Von Neumann reportedly summed the series in his head anyway.)
Source: Classic puzzle in wide circulation, famous for the anecdote in which it was posed to John von Neumann. Statement written for AxiomIQ.