The lights went out the other night. If you have an analog clock and a digital clock, this allows you to determine when the lights went out and when they came back on. In this case, the analog clock was almost identical to my watch, so the lights were not out for very long. To make this problem more interesting, I will make up some numbers.

Suppose that the digital clock reads 3:30, the analog clock reads 6:30, and the watch is at 7:00. From the digital clock, we know the blackout ended 3½ hours ago, so the lights went on at 3:30. When did the lights go out?

I am not interested in the answer so much as the method you use to find it. My initial way of solving the problem was much more complicated than it needed to be. I want to see if you can find the really easy method of determining the answer, which I found to be somewhat counterintuitive, for reasons that I will give later. Be warned that I have presented the problem so as to encourage you to use the same faulty method I used.