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Lepton
1:41+ Arse Scratcher

 Posted: Sun Dec 14, 2008 9:43 am    Post subject: 1 When I was young, my parents used to hang outdoor Christmas lights on our house. They had some boxes that would turn on and off the lights automatically. I used to try to connect the boxes in funny ways so that the lights would go on and off at unpredictable times. The boxes worked like this: they had a 24-hour dial on the front that would spin around once per day. You put in little green triangles and little red triangles at hour increments along the dial. The boxes plugged into electrical outlets and had a jack above the dial into which the lights would be plugged. As the dial turned, it would switch on when it reached a green triangle and of when it reached a red triangle. For example, if I put a green plug at 14:00 and a red plug at 20:00, the box would conduct electricity after 14:00 and it would stop at 20:00. My first discovery was that, but plugging one box into another, I could turn on the lights for just one hour every 24 days. Using 2 of the boxes and just 4 green and 4 red triangles, what is the longest series of on/off periods that you can make such that no period is the length of a previous period?
Zag
Tired of his old title

 Posted: Thu Dec 18, 2008 5:03 pm    Post subject: 2 I only need 3 red and 3 green. Set the first one to be on for (6 hours + x) where x <= 1 minute), off for 6 hours, then on for 6 hours. Set the second one to be on for 6 hours, but not to start the first on period until 6 hours after we first give it power. Every day the second one will advance by 12 hours + x on its clock. The effect is that every other day it will show twice, with the overlap moving backwards by 2x. Day 1: off for 6 hours, on for x, off for 6 hours, on for (6 hours -x) Day 2: off Day 3: off for (6 hours - 2x), on for 3x, off for 6 hours, on for (6 hours - 3x) etc. As x goes to zero, the number of different times before this repeats goes to infinity.
ralphmerridew
Daedalian Member

 Posted: Fri Dec 19, 2008 2:02 am    Post subject: 3 If it's like the one's I've seen, you can only set it on integral hours.
Daedalian Member

Posted: Mon Jun 01, 2009 4:34 am    Post subject: 4

 ralphmerridew wrote: If it's like the one's I've seen, you can only set it on integral hours.

This is typical. Many allow 30- or 15-minute intervals, but I don't recall seeing less [with the analog types].
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