For some reason, this took me a lot longer to figure out than it should have, I must be getting old(er).
Anyway. What you need to do is complete a puzzle by only pressing the left mouse button once and then holding it and dragging to fill in the rest of the squares without lifting your finger. You can retrace your steps without cancelling what you have drawn but you cannot draw diagonal lines or fill in squares without an adjacent block.
Not all puzzles can be completed this way but almost all of the Tiny puzzles are applicable. Any from the first page are good candidates, especially if you've already completed them and can see the solution before opening the level.