Four safety engineers set out to inspect a newly cut tunnel through Mt. Popocaterpillar in the Andes. Each person walks at a different constant integer speed measured in meters per minute. In the tunnel there is a mine car which travels along a fixed track, automatically going from end to end at a fixed integer speed. When people board the car they may reverse its direction, but cannot change its speed.
At noon on Monday all four engineers start at the south end, while the mine car starts at the north end. The first (fastest) engineer meets the car, and takes it some distance north. The engineer gets out and continues going north, while the car resumes heading south. Then the second engineer meets the car and also takes it some distance north. Likewise for the third and fourth engineers. All the people, and the mine car, travel continuously with no pauses. The inspectors always go north. Each person enters and exits the car at an integral number of minutes.
All four engineers reach the end of the tunnel simultaneously. What is the earliest time this could happen?
Lately, I've been working on this puzzle, left unsolved more than one year ago. It's a tough puzzle.
Based on Excel, I have reached three suitable solutions, that conforms to all the conditions of the puzzle, including (and this is the toughest to satisfy) that the engineers be walking, which means that they are under 180 (or so) meters/minute. The lower of these three is the solution, although I am not going to disclose it here. AFAIK, by now the solution is not accessible on the internet, and I think it is better to keep it that way (if I had found solution on the internet, I know I would have relinquish the puzzle).
To check a possible solution with mine: in my solution you need only three of the ten digits to express the speed of the four engineers (for example: 107, 100, 71, 70) meters/minute…). If this is possible: then odds are that both solutions are the same; otherwise they are surely different (this has nothing to do with the resolution of the puzzle, it's just a useful way to check both solutions).
Edited on July 20, 2020, 4:12 pm
Reedited with substantial changes on
Edited on August 11, 2020, 8:27 am
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Posted by armando
on 2020-07-20 16:09:57 |
Solution (but hidden...)
