Traffic lights at three different crossings on a road after every 10 minutes,15 mintues and 20 mintues, respectively. If they change together at 9.am first, when they change together again
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So you’re now the getaway driver planning a bank heist in a town with very strange traffic light timings, and you think “oh, darned, should have paid attention in class” and also “but that’s what Quora’s for.”
I used to review test problems, so I look for ambiguities, and “change together” is one such.
One possible answer is every hour on the hour, if by “change together” you simply mean switch colors at the same time. But if you’re the getaway driver and you pick 10am, then you will get stuck at the third light because while the first and second lights changed an even number of times and so (assuming they all switched to green at 9am) switched back to green, the third light changed an odd number of times to red. Busted!
If by “change together” you mean change to the same color at the same time, then the timings are actually 20 minutes, 30 minutes, and 40 minutes, and the answer is every two hours.
Now the final question is whether you can get a clear getaway through all three green lights at all. Incomplete information. If the lights changed together to green at 9am, then yes, but if the lights changed together to red at 9am, then they’ll never change to green at the same time, and you have a different problem of what times will all three lights be green.
Thanks for the A2A!
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