1

Consider the following problem:

Emma has three time switches. Every switch that is turned on allows an electric current to flow for three hours, then it blocks the current for three hours, allows it again for three hours, blocks it again for three hours, etcetera. The clocks only run when the current is on. Emma now puts the time switches in series with a lamp, and synchronizes them, to make sure that all three start on a three hour period of allowing the current to flow. How many hours will the lamp be burning the coming week?

I have difficulty understanding this problem. To me it just seems the lamp will be burning for 84 hours, since the 3 switches are synchronized, but this doesn't seem to be correct. What am I missing here?

MacropusRufus
  • 219
  • 5
    I presume the complication is that after three hours, the first switch will shut off, and then no power reaches the next two switches, so their clocks shut off. Then, three hours later, the first switch opens up, and electricity can again reach the second switch. But then the second switch's clock starts running, begin its 3 hour period of blocking current (since it isn't aware that three hours have passed). Then three hours later, both switches shut off again, and then the first switch opens, and electricity reaches the second, and now it opens, and now electricity reaches the third... – Elchanan Solomon Feb 16 '13 at 21:41
  • @IsaacSolomon Ah, that makes sense – MacropusRufus Feb 16 '13 at 21:47

0 Answers0