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there's a few values you can play around to make avgLDR behave differently. In line #179 there's this:

readOut = map(analogRead(pinLDR), 0, 1023, 220, 0);

0 - 1023 is the "raw" value of your LDR. This is then mapped to 220 - 0. Try to vary the ranges a bit, for example:

readOut = map(analogRead(pinLDR), 0, 1023, 220, 60);

This might shift avgLDR to more usable values. Another way might be decreasing the 0-1023 range. Basic principle is:

Current brightness (160/190/240 are defaults) - avgLDR = brightness to use. So if your lowest value at daylight is already around 80 you'll only get 160 brigthness on max level (240 - 80 = 160).

Edit: Don't have one of the clocks with an LDR at hand right now, so I can't really test this for some values.