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The digital clock segment brightness challenge

written on 2023-01-03, last updated on 2023-01-04

It is the middle of the night. You are sitting in your kitchen. The only source of light is the digital clock on your oven, telling the time with 4 bright digits. But the clock is behind you, so you cannot see it. You can only see the wall and furniture opposite you, weakly illuminated by the digital clock.

Every minute, the brightness of the clock light shining onto your kitchen changes slightly, as time advances. Some numbers are brighter, since they use more of the available 7 segments.

11:11 is the least bright time (8 segments are on). 88:88 would be the brightest number (28 segments), but is doesn't exist as a time. So 08:08 (26 segments) may be the brightest.

Unable to sleep, you are wondering if it is possible to actually know the time, just be looking at the diffuse brightness on the wall opposite you.

Questions

  • is it theoretically possible to tell the time, just by looking at the level of light sent out by the clock?
  • how long would you need to stare at the wall? 2 minutes? 20 minutes? Even hours?
  • how could this be implemented as a computer program, given perfectly clean brightness levels (from 8 to 26) for each minute as input?
  • how could it be done with only relative changes of brightness from one minute to another?
  • how could it be done with a noisy video of the wall and furniture, with a constantly changing, auto-adjusted camera aperture?

I intend to revisit and solve the above questions whenever there is time and I feel like it.

Answers