Ahh hah! Got it. And didn't have to make every block green, either.
The way I got it (thanks for the tip JoNo) was to start at the top right and click. That makes the top two blocks of the far right column green. So move down so that your next click will make the next 3 blocks green, and repeat until the entire column is green. Then move over two rows, and click one to the left of every dark block, moving up to the top until the second column is green. THen over two rows and back down, again clicking one to the left of every dark block so your third column is green. Repeat in this pattern until you get to where you're clicking on the very last column. That opened it for me, even though 4 blocks were left black.