I know exactly how you feel staring at that Reactor grid while the numbers blur together. It gave me a splitting headache too, so I wrote down the exact sequence that finally cracked it. It may not be the prettiest solution, but it works — and sometimes that is all you need to move on.
Before you touch a single switch: reset the grid. I cannot stress this enough. If you start from a half-solved state, the sequence below will not land the way it should, and you will just end up more frustrated than when you started.
The Reactor Solution, Step by Step
Here is the part that tripped me up more than anything else — several fields share the same name. If you just read the labels and start flipping, you will almost certainly hit the wrong node. Use the short description next to each name to identify the right one, and work through the list in order.

| No. | Name | Description |
|---|---|---|
| 1 | 10B1 | upper left, inside |
| 2 | 10B3 | lower left, inside |
| 3 | 10B2 | middle left, inside |
| 4 | 10B4 | bottom left, outwards |
| 5 | 10C1 | topmost |
| 6 | 10C2 | middle top |
| 7 | 10C1 | topmost |
| 8 | 10C2 | middle top |
| 9 | 10B4 | top right, inside |
| 10 | 10B3 | top right, inside |
| 11 | 10B1 | lower right, inside |
| 12 | 10C1 | topmost |
| 13 | 10C1 | topmost |
| 14 | 10A1 | lower right |
| 15 | 10C3 | middle |
| 16 | 10C2 | middle top |
| 17 | 10C1 | middle top |
Notice how many times 10C1 and 10C2 come back around, and how the same name can appear at different spots on the board — that is exactly why the description column matters more than the label. I kept the descriptions short and positional on purpose, so as long as you match the spot rather than the name alone, you will stay on track. Some of these look like duplicates at first glance; they are not the same node, so do not skip a repeated name just because you already pressed one like it.