Friday, January 19, 2018

mathematics - Connecting 3 circular power timers to lights so that they turn for one day on Christmas


My friend gave a question to me. I am not sure if it is an original puzzle, but he has 2 lines of Christmas lights and 3 circular timers with 96 switches apiece. Each switch turns on power for 15 minutes.



How can you arrange the timers, switches and lights — as far in advance as possible — so that lights would be on for 24 hours on Christmas day?




  • All lights are off for the last 15 minutes before Christmas.




  • For the next 24 hours, some lights are on at each point in time. (Some may also be off.)





  • All lights are off again for the 15 minutes after that.




No constraints outside of the 24 1/2 hours just described, except:



  • Any 24-hour interval before Christmas has all lights off for at least 15 minutes.


One timer may plug into another.



The timers operate as in this video. I am sure a lot of you have seen them in real life.


Note: This gem of a puzzle was given a make-over after a year and a half of being closed. The original poster might not be around to officially accept a solution. (Attempts were made to reach the poster half a year ago.)




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