So I know, there's a thread about Shroud puzzles like, every other week.
But the solution is usually the same, like: solve down, and then USE THIS CHART.
That's a bother for me, because I hate memorizing charts and stuff. Double so, because if I forget a detail (and that does happen), there's no quick way to fix it, it's either alt-tab to google and quick search, try random buttons or try to figure out the solution (which ends up trying random buttons, except with more thinking behind it), and either of those can easily take a minute or two.
So I hate that way enough that I spent some hours coming up with something better, or at least less memorization dependent.
Now, this isn't for everyone. If you already know THE CHART by heart, you're probably fine sticking to it. If you like to alt-tab, no problem. If you have a solver on your laptop/mobile phone, excellent.
But if you like to use your head, but then you get to the bottom row and it's time to USE THE DREADED CHART and you forgot how it looks or where you put the one you printed... then this is for you.
So, without further ado, the guide:
Important concept: solving down - starting with the top row, if some button is unlit, click the button under it. You can run on row 3 and below all you want, and actually, running over row 2 is no problem either, just fix up the top row afterwards. Repeat this row by row. This solves all but the bottom row of the puzzle. (And sometimes solves the whole puzzle).
For the 3x3:
Step 1: solve down.
Step 2: solve up.
Step 3: solve down.
For the 4x4:
Step 1:solve down.
For the 5x5:
Step 1: solve down.
Step 2: solve the bottom row using the buttons in the bottom row. You're "messing up" the second-to-last row, but that's good.
If you're unsure how to do this, imagine the bottom row as a separate 1x5 puzzle, and solve left (or right).
Step 3: if the pattern you got before 2 was not symmetrical (eg. X0XX0) hit the middle button in bottom row. "to restore the ballance" so to speak.
Step 4: solve up.
Note: If that sounds confusing see Cauthey's re-phrasing of it in post #6 below, maybe it'll make it clearer.
Note2: if you forget step 3 don't worry. It's only there to speed it up. Without it can just repeat the procedure a couple of times. (The second fastest way is to "swap up and down" after step 2 and go back to step 1).
Circle (kind of unrelated, but included for completeness):
Step 1: solve clockwise until there's just one dark spot.
Step 2: step on the single spot.
Step 3: chase one the dark spots around, for example clockwise.
I've been using this way for a couple months, and while it ends up using more button presses than the others, it tends to be very fast, because you can just keep hitting the buttons with minimal thinking. There's also no pause to consult the chart and no running back to the top.
If someone is present while I'm solving a puzzle, I often get tells/voice comments like "woah", "GJ on that puzzle" or "now that was damm fast". The whole solving of 5x5 takes me less than alt-tabbing to a browser.