It sounds incredibly stupid, but the most difficult puzzle game I’ve ever enjoyed playing is about cooking sausages on both sides.
You and your massive grilling utensil are stuck in a land full of sausages and grills, and you have to cook every sausage on both sides. Each sausage, as well as the player, is two grid squares long and one wide, which makes positioning…a challenge. In fact, I’d say positioning objects properly within the level is the entire point of the game.
You cook the sausages by moving them around, rolling them onto grills in the ground. Each sausage has to be cooked on its two sides, but if you cook any side more than once, it gets burnt and the level is failed.
You’ll quickly learn tricks like moving backwards to get into the right position to rotate just the right way to move a sausage to the correct position while also setting yourself up for the next move. I wish I could do it justice, but the difficulty is really better experienced than heard about secondhand.
The difficulty ramps up quickly, and elements like ladders are introduced to make the puzzles three-dimensional, and just that much harder. Solving every puzzle on the island is incredibly difficult, and unlike a game like, say, Fez, there’s no flashy ending. The meat of the game (so to speak) is the puzzles themselves, which are sincerely enjoyable and truly among the most challenging I’ve ever seen in a game.
You like hard puzzle games, grid-based positioning challenges, or frustration.