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SciAm clock puzzle

October 15, 2025 at 5:10 PM by Dr. Drang

Scientific American published a clock puzzle a couple of weeks ago that I finally got around to looking at today. It wasn’t hard, but I’m less interested in the solution than in a very small discrepancy I found. Finding discrepancies was a big part of my job, so it was nice to see that I still can.

Before we go any further, you should know there will be spoilers—there’s no way around that. So if you want to solve it on your own, stop here and click the link in the previous paragraph.

The puzzle concerns this clock face:

Original clock orientation

The hour, minute, and second hands are all the same size, there are no numerals, and the clock has been rotated. Your job is to determine the time. I’m going to add some blank space here so people who want to work out the answer don’t accidentally see it.

OK, the answer is 4:50:00, and what bothered me was the position of the hour hand. I thought it was too close to the 5 o’clock tick. Fifty minutes is five-sixths of an hour, which means the hour hand should be

56⋅5=4.1667

thin minute ticks past the bold 4 tick. Doesn’t it look a little further than that to you? Somewhat more than one-sixth of the way from the thin tick to the thick one?

So I took a screenshot of the clock face and imported it into OmniGraffle. I rotated the face 75° so the second hand is pointing straight up. Then I started drawing lines on the face.

Full rotated clock

First, I drew horizontal and vertical lines in red to make sure the 75° rotation was correct. It was. Then I added an orange line where I thought the hour hand should be. The hour hand moves 30° every hour and 5° every 10 minutes, so the hour hand should be

4⋅30°+5⋅5°=145°

clockwise from the 12:00 position. It was definitely not aligned with the hour hand (I’ll show you a zoomed-in view in a minute). To further insure I had the clock face oriented properly, I then drew a blue line at 144°, which is where the 24-minute tick mark should be.1 They lined up well.

Finally, I drew a magenta line at 146°. That was a little off from the hour hand, so I adjusted it down to 145.9°. Here’s the zoomed-in view so you can see where all these lines are:

Zoom in on rotated clock

So yes, the hour hand is a little off, nearly twice as far from the 24-minute tick as it should be. I can still find discrepancies, whether there’s any value in it or not.

I’ll leave it to you to decide whether I would have written this post if it had turned out I was wrong.

  1. Minute ticks are 6° apart, so 24 minutes is 144° clockwise from straight up. ↩

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