This is pretty fun.
In a reflex, I started dragging instead of clicking to make lines appear. :P
Some suggestions if you're still going to work on it:
- Higher res version? This looks small even on my lappy's rather modest 1366x768 resolution.
- There should be a big "submit answer" button which automatically generates a new level for you if it's correct.
- A high score to proudly post here? Like +10 points for every puzzle solved, -5 for every wrong answer.
- The randomizer doesn't get rid of your inputted lines.
- Being able to set a grid size for a bigger challenge? If you're going to have a scoreboard, the score could be relative to the grid size.
- Maybe some sound effects! The <audio> tag is perfect for this.