Est. 1998 — 27 years of woodworking knowledge
Friday Puzzler -- Lighthouses
Alex Y
There are three lighthouses visible from the same place. One cycles on for 3 seconds, then off for 3 seconds. Another cycles on and off for 4 seconds each, while the third cycles on and off for 5 seconds each.
Assuming they all turn on at a certain point in time, how long will it be until:
1) they are all off
2) they all turn on again at the same time
3) they all turn off at the same time
Re: Friday Puzzler -- Lighthouses
Larry Barrett
The answer to the first question, how long until they are all off, is 6 seconds.
The answer to the next two questions is interesting. if, as the problem states, they all come on at the same time and then start their individual sequences, then there is a time when they will all come on at the same instant (several times each hour). There is also a time(s) when the first and third go off at the same instant, but I think there is no time when all three go off at the same instant.
Re: Friday Puzzler -- Lighthouses
Henry Higginbotham
I may misunderstand the rules, but I get 15 seconds as the first point at which they are all off, and 120 seconds as the next time they all turn on together. The 3-second and 5-second lights always turn off at an odd number of seconds and the 4-second light at even times, so I agree that they can never turn off at the same time. If 120 is correct, then any events of any sort would have to happen in that first two minutes.
[Mostly] Correct!
Alex Y
And yes, the third question was a trick question, which you properly reasoned.
But both you and Henry have missed the first part.
Correct on parts 2 & 3
Re: [Mostly] Correct!
Larry Barrett
I think the three sequences look like this:
111000111000111000...
11110000111100001111...
11111000001111100000....
So they are all off at the 6 sec mark (and again at 16 sec).
Re: [Mostly] Correct!
Alex Y
Your reasoning is correct, but they initially all turn on at t=0, not t=1.
Re: [Mostly] Correct!
Henry Higginbotham
Assuming the answer can't be at an instant when a light is turning on or off, how about 5.01 (or thereabouts), for the first time they're all off?
Correct!