Est. 1998 — 27 years of woodworking knowledge
Friday Puzzler -- Lighthouses
Alex Y
There are three light houses on a shore. They flash with different frequencies; one is 3 seconds on and 3 off, another is 4 on and 4 off, and the third is 5 on and 5 off.
If they all turn on at time zero, when will it next be dark (none on). When will they next all three come on at the same time?
Re: Friday Puzzler -- Lighthouses
Sam Force
When it goes dark because all lights are off is quick, the 1st time the light on a 5 second relay goes dark the others are also dark. To get them all turning on at the same time I believe would be on double time plus 1 so I think the relays align at 121
Re: Friday Puzzler -- Lighthouses
Alex Y
Why the +1?
Otherwise correct.
Re: Friday Puzzler -- Lighthouses
Sam Force
My thinking was, at what time would they all turn on at the same time? That eliminates using the 3_4_5 sequence and makes it a 6_8_10, so in my mind double time plus 1 would be the 1st time they all came on at the same time....121
Re: Friday Puzzler -- Lighthouses
Alex Y
You are correct that the complete on-off cycles are 6, 8, and 10 seconds long. But can you explain what you mean by"double time"? Given the result, I suspect it is what I would refer to by the initials"lcm", which is correct. But at 120 the 5-second light would have gone through 12 complete cycles, and will start its 13th cycle. By 121, it and all the others will have already been lit for 1 second.
Re: Friday Puzzler -- Lighthouses
Sam Force
My thinking was at 120 seconds they would all be in the last second of being off. And at second 121 they would all turn on to start a new cycle. Might not be right but I think it is
Re: Friday Puzzler -- Lighthouses
Alex Y
for the lighthouse with 5-second on and off:
at t=0, the light comes on (if it initially came on at t=1, 121 would be the correct answer)
It stays on for 5 seconds, i.e., until t=5
At t=5 it turns off
It says off for 5 seconds, i.e., from t=5 to t=10
At t=10 it turns on again.
Repeat 11 more times
At t=120, the twelfth dark period ends, by the light turning on.
At t=121, it will have been lit for 1 second already.
The least common multiple (LCM) of 6, 8, and 10 is 120.