On the coast there are 3 lighthouses. All 3 turn on at time zero.
- The first light shines for 3 seconds, then is off for 3 seconds.
- The second light shines for 4 seconds, and then is off for 4 seconds.
- The third light shines for 5 seconds, then is off for 5 seconds.
When is the first time all the lights will be off at the same time?
(In reply to
Solution by Jer)
I interpreted this problem a bit more strictly. Since all the lights were turned on at the same time, I sought a time when all the lights went from on-to-off at the same time.
But this was impossible:
Just the first two lights: the first light turns from on-to-off at 6m+3 seconds, with m an integer and the second light turns from on-to-off at 8n+4 seconds, with n an integer.
Then I would need 6m+3=8n+4 over integers, but the left side is always odd and the right side is always even so no solutions exist.
re: Solution
