The Witness throws a stack of tough puzzle variations at you in the Quarry.
The Witness: solving the Quarry puzzles
Quarry is one of the tougher zones of The Witness. You'll want to have mastered the tetromino puzzles of the Marsh, the coloured star pairs of the Treehouses and the colour quarantine puzzles of the Bunker as well as the basic hit the dots and black white quarantine variations.
One top of all this, the Quarry has its own variation - the grace engine. Someone told me we should call it "eliminator", which is admittedly more communicative, but my name is poetic so you're stuck with it. Enjoy that.
Quarry - factory
Facing out to sea in the Quarry, the factory is the large structure on the left.
The door is locked with a twin puzzle; here's the solution, screenshotted as it slid rapidly out of view.
Inside you'll find a terminal with a grace engine puzzle. Notice how when you miss one of the targets (a dot you're "supposed" to hit, or a black white quarantine square), the grace engine logo and the missed target cancel each other out, resulting in a valid solution. Think of that little three-pronged symbol as a saving grace, or get out of jail card for one mistake - only it's a mistake you need to make, to fire up the grace engine.
There are two grace engine terminals in this room that power devices - a ramp and a lift. You need to use these to climb across the room so you can reach the terminal arrays. The first set, between the two terminals, is a grace engine tutorial bank, but the ones beyond throw colour quarantine into the mix to make things trickier. When all the puzzles on the catwalk are solved, set the lift and ramp so you can climb back down, then cross the stream to the sawmill.
Quarry - sawmill
To kick things off in the Sawmill you need to solve a very tricky pair of puzzles with a slanted tetronimo challenge on one side and a coloured star pair set on the other; this is The Witness telling you to do the Marsh and Treehouses before you try this shizzle. The solutions are linked in the previous sentence.
This powers a slider you can use to raise a ramp to the level above, where you can solve a new terminal array of puzzles with a mix of variations.
When you've completed this set, use the nearby controller to move the machinery to the final position; hop on as it cruises past and use it to reach the stairway to the next array.
Quarry - firing the laser
After all puzzle arrays are completed in the sawmill, climb on up to the roof of the factory; you can take the lift or go back through the grace engine puzzle area and open an optional door to take some stairs. Or you can leave the Quarry and climb over the rocks from the Desert Ruins side, even.
Power the laser with the simple puzzle board (solution) and relax in the knowledge of a job well done.