I know Chaco's already solved this room by now, but we just *know* this room is going to come up over and over again, so I figure I might as well go over this room. I won't put up a full walkthrough, but I will go over what this type of puzzle involves, as well as the information necessary to go through the steps to solve it.
×This is a SIGMA+ puzzle variant. I'm not going to prove whether there's a 1-to-1 mapping or not between every configuration of orbs you hit to every configuration of gates that could be open, because that's both unnecessary and far too much work. Suffice to say though that even if you have all the gates closed but one or two in a certain area, your problem could be *anywhere* in the orb grid, not just in the area you're working on.
Fortunately, because of the way SIGMA+ puzzles work, it doesn't matter which order you hit the orbs. And because they're strictly toggles, all that matters is if you hit an orb or not.
So, having one gate left open might mean you have a whole load of orbs wrongly toggled. And searching all 16 million ways to hit the orbs is just silly. So, how to deal with this? Well:
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×The classical method for solving a standard SIGMA+ puzzle variant is to tackle each row or column alone. This is sometimes called "
light chasing"
. Since each orb only toggles its neighbours, you can close all of the first row's gate using only the second row or orbs. You can continue through the rows until you reach the last row. Note that there's only *one* way to hit each row's orb to close off all of the previous row's gates, so there's no guesswork involved in this part.
This will only net you a solution for rare configurations. More likely (and certainly in this case), you will be left with some still open gates on the last row. This means that the one row we left untouched (the first row) is the culprit. Unless you know exactly how the SIGMA+ pattern and the orbs coincide, all you can hope to do is to go through every combination of orbs in the first row and then "
chase"
the open gates back from the top down again, until you find the combination that works.
One more general hint, and then a final big hint (that'll basically tell you how to start that'll lead to a solution pretty quickly).
The general hint (that you should've already worked out from the above before I even say it):
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×There's 6 orbs/gates to a row. There's 4 orbs/gates to a column. Do columns rather than rows. (You should be doing this anyways since there's nowhere near as much walking to complete a column). This reduces the number of configurations you must test to 16.
The specific way to start to solve this room first time:
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×Start from the right, heading left. The only orb on the far right column you should ever hit is the topmost one.
It just happens to fit.