Hi, I think there's currently a bug for Puzzle 55 on version 2.0.2! I'm not able to logically mark any tiles right from the start. I love this game though! Currently at 60/200 completed!
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In this puzzle and others when you don‘t know what to do next, find a longer block and try placing it in a corner. Often you’ll find that it will contradict with the next line once you continue from there and you’ll be able to cross out the corner square. You can also see this technique illustrated in the "mouth part" of the tutorial.
If you have to draw a bit to clearly see the contradiction, you’ll be able to remove the wrong parts with the undo action afterwards.