Deponia

During the first part of the game, after you've knocked Goal off of the Organon Cruiser, you need to rescue her from the mayor's town hall. This comes with making sure no one else takes her to their house. In order to do this, you have to make it so their houses are unsafe for her to be kept in, and this is tied to a puzzle elsewhere. The steps:

1) Have Goal be kept in the Town Hall, which is story related. You will need a ticket to plead your case with the mayor, which will place you at #66 in the queue. Those in front of you are the three gentlemen on the bench in the foreground.
2) On the same screen as the three gentlemen is a bulletin board with three target magnets holding up important documents. Take these magnets, as you will need them to solve the puzzle.
3) Exit the Town Hall and, on the village screen, go through the Alley.
* MAKE A SAVE HERE JUST IN CASE YOU MESS UP *
4) The detonation board here is the puzzle, but it wouldn't hurt to listen to the explanation as to how it works just the make sure. Basically, using your magnets, you're going to mark on the board where they will set the next bombs to excavate for more trash.
5) The three targets, using the magnets on the board, will be the three houses of the gentlemen from Step 1. They are: the two houses in the middle on the top row, as well as the house in the lower right on the bottom row. These are related to the actual hats that the gentlemen were wearing, thus why you know those're the right locations.
6) With the magnets in place, exit out of the map and hit the bell right next to the board. The excavation will commence and when you exit, those three houses should be signing an alarm from the bombs. The trophy should trigger at this point if you marked them correctly.