The puzzle, as previously presented:
After getting a new alarm clock for our master bedroom, I determined that the clock is entirely too bright. It kept me awake for most of the night, as every minute it changed the time and burned a new pattern in to my retinas. As I laid there, unable to sleep, I started thinking “Is this it? Is this the brightest time I am going to see? Can it get any worse?”
This week’s puzzle of the week comes in two parts. The first part is straightforward – what times, as presented on the clock’s LED face, are the brightest and the dimmest? Assume that each segment gives off the same amount of sleep-depriving light, and that the clock represents civilian-time (and not 24-hour time.) The second part of this week’s puzzle is a little more challenging – what 90 minute periods (i.e., from 2:04 to 3:33, etc.) represent the clock’s dimmest and brightest periods? That is, when do I have the best shot at shuteye, and when should I not even try?
Many thanks to everyone that attempted the puzzle this week, and submitted a solution. As it turns out, the brightest single time presented on the clock’s LED face was 10:08, and the dimmest was 1:11. My best chance for some REM sleep (the dimmest overall 90 minutes) is from 1:00 to 2:29, and I shouldn’t even think about closing my eyes from 9:30 to 10:59, the brightest overall hour. These were proven by many people with Excel solutions, and Jenny Ross even went so far as to graph them for us!
After seeing the answers, they make intuitive sense — “1” is the dimmest single hour entry, so the 90 minute segment should cover it completely. The “2” hour after it is dimmer than then “12” hour before it, so 1:00 to 2:29 is the dimmest period. Similarly, “10” is the brightest single hour entry, and “9” is brighter than “11,” so 9:30 to 10:59 is the brightest 90 minute segment.
Congratulations to Colin Gillespie, the randomly selected correct entry, and winner of this week’s $50 ThinkGeek gift certificate! Many thanks to everyone that submitted and entry.