Puzzle time - bugs on a ruler

[jon-nyc]

24 tiny bugs are placed randomly on a meter-long ruler; each bug is facing toward one end or the other with equal probability. At a signal, they proceed to march forward (that is, in whatever direction they are facing) at 1 cm/sec; whenever two bugs collide, they reverse directions.

How long does it take before you can be certain that all the bugs are off the rod?

[Klaus]

I would like to congratulate you for formulating the puzzle using the metric system.

[Klaus]

I do note that 24 = 4! . Is that a coincidence?

[jon-nyc]

I'm a fan of the metric system except for temperature, where Fahrenheit is so obviously superior.

[Klaus]

@jon-nyc said in Puzzle time - bugs on a ruler:

whenever two bugs collide, they reverse directions.

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Maybe I misunderstand something but why is that relevant? Isn't that equivalent to the bugs not colliding and just continuing their travel?

If that is so, I'd say the answer is simply 100s (the maximum time it takes for a single bug).

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[Axtremus]

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Without trying to tighten the lower bound, I would say a comfortable upper bound is something like (half the # of bugs) * (time for one bug to travel the full length of the rod twice), so 12 * 200 seconds = 2400 seconds.

Worst case (maybe worse than the actual realizable worst case) is the remaining bugs keep colliding while the two "outermost" bugs are walking off the rod. One outermost bug would take at most 200 seconds (allows for one collision for the worst case) to completely walk off the rod, and there are 12 "pairs" of "outermost bugs" to work through. So 12 * 200 seconds = 2400 seconds at most.

The results can definitely be improved upon but I think it will not get any worse than 2400 seconds.

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[jon-nyc]

Klaus

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You got it.

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