Puzzles
A fly bounces between two approaching trains until it's crushed — how far did it fly?
Two trains, 60 miles apart, race toward each other on the same track — one at 20 mph, the other at 30 mph. The instant they start, a tireless fly departs from the front of one train at 40 mph, flies to the other, bounces straight back, and keeps shuttling between them until the trains collide. How far does the fly travel in total?
Reveal the answer
48 miles. The trains close the 60-mile gap at a combined 50 mph, so they collide in 1.2 hours; the fly, flying the whole time at a constant 40 mph, covers 40 × 1.2 = 48 miles — no need to sum an infinite series of ever-shorter bounces. John von Neumann is said to have solved a version of this instantly this way, though his biographers suspect the anecdote (like many about him) has grown taller in the retelling.