Notice that you must enter the "21" from the right corner square; any other approach will leave that square untouched. This means that you must leave the "10" to the right or that square will never be touched. Stroke 12 must go up only one square and then turn right to touch the white square above the "21". We don’t know how far the dotted vertical lines go, but we certainly can't afford to have many more of those one-square steps if we want to do the full circuit in 21 strokes.

The stroke that enters the "10" must come from above; otherwise, the straight-line stroke would not end at the "10." We know that the dotted line going into the "10" can't be longer than two squares or it would isolate the white square above the "12."

You will turn nine times between the "0" and the "10." If you start by leaving the "0" horizontally, you'll enter the "10" from above; if you start by leaving the "0" vertically, you'll enter the "10" from the left. Your first stroke must go to the right.