The Puzzle: Two trains are 100 km apart and are traveling toward each other on the same track.
- Each train travels at 50 km/h.
- A bee starts at the front of one train and flies toward the other at 100 km/h.
- When it reaches the second train, it immediately turns around and flies back to the first.
- It continues this until the trains collide. What is the total distance the bee has traveled?
1. The Complex Mistake
Many people try to calculate the distance of each individual “leg” of the bee’s journey. This leads to an infinite geometric series: d₁ + d₂ + d₃ … While mathematically possible, it is extremely difficult to do in your head.
2. The Simple “Aha!” Moment
Ignore the bee’s turns. Focus on Time.
- Relative Speed of Trains: 50 + 50 = 100 km/h.
- Time until Collision: Distance / Speed = 100 / 100 = 1 hour.
- The bee is flying for exactly 1 hour at a constant speed of 100 km/h.
- Distance formula: Speed × Time = 100 km/h × 1 h = 100 km.
3. Result
The bee traveled exactly 100 km.
Interview-Focused Questions
Q: Have you heard the story about John von Neumann and this puzzle?
A: Yes. When John von Neumann (the famous mathematician) was asked this, he solved it in seconds. When asked if he knew the “shortcut”, he replied: “What shortcut? I just summed the infinite series.” This is a fun way to show that even if you can do the hard math, the logical shortcut is usually the “engineer’s” preferred path.
Q: What if one train stops?
A: The logic remains the same. Calculate the time it takes for the moving train to cover the distance, then multiply by the bee’s speed.
Key Takeaway
This is a lesson in Problem Selection. Don’t solve the hard problem (the distances) if you can solve the easy problem (the time) that gives the same answer.
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