Make sure 'layout' is selected then edit the layout of the puzzle as appropriate by left mouse clicking to remove or add blocks of the puzzle.
Change to 'lights' then set up the lights of the puzzle as they appear in front of you.
WARNING: not all puzzles are solvable.
If you just change the layout, fill in the default lights lit, and hit solve first, it will let you know if its solvable, if a warning pops, it is not solvable, if it does not, then it is.
If you can't solve then beat down the boss (about 10%) and a panel will lock. You will notice a tile go darker, it may be lit, it may not be. Treat the locked spots as if they don't exist in the layout. Go back to layout mode, remove the locked tiles, and solve again. If you have to lock tiles, the extra chest at the end will not open for you.