Its fame is born from a gentle trap: intuition pushes towards an endless calculation of twists and turns, but the problem has a much more direct solution.
The fly between two trains
Riddle statement
Two trains are 300 km apart and are moving towards each other, each at 60 km/h.
A fly leaves the first train towards the second at 90 km/h. Every time it touches one train, it instantly turns and flies toward the other, repeating the process until the trains collide.
What total distance does the fly travel?
Show solution
Solution
Answer: 225 km.
The two trains are moving towards each other at 60 km/h each, so they are approaching at a combined speed of 120 km/h. The time until the collision is:
During that entire time, the fly flies non-stop at 90 km/h. The total distance traveled is:
There is no need to add infinite sections: the series converges, but it never has to be calculated.