All the levels are solvable I have beaten them all. If you are having some troubles there are walkthroughs online or you can try and play the cool math games version of the game.
Yeah, 1-11 is literally glitched, but you can only see it in full screen mode. I dunno what happened between playtesting and posting, but it's glitched now.
When the green box is placed on the button in the top left, the gate sprite disappears, but the hitbox remains.
Edit: You can brute force it by mashing the arrow keys, so technically it's not a problem???