This puzzle requires quite a bit of logic. First, it is easy to tell that exactly 5 of the LCDs are always off; these all belong in the leftmost digit, which is of course either blank or 1.

The two rightmost segments of that digit are either both on or both off. Looking at the on/off patterns of the 23 “interesting” segments, you can note that there are only four patterns that are duplicated and therefore possibilities for that leftmost digit: 00011, 01110, 10101, and 11111. 10101 cannot be the sequence, as it would take at least 21 hours to produce it. 11111 and 01110 can be ruled out with a little more effort by noting that they would place unreasonable requirements on other duplicate patterns.

We now know the following:

- The fifth pattern is for a time between 10:01 and 12:59, showing 13 LCDs
- The fourth pattern is for a time between 10:00 and 11:29, showing 14 LCDs
- The third pattern is for a time between 7:01 and 9:59, showing 14 LCDs
- The fourth time is the average of the third and fifth times

Using this information, we can migrate the puzzle to a more tractable combinatorical problem. Here is the puzzle completely worked out:

That last set of LCDs looks like the Loch Ness Monster (NESSIE) if you squint at it.