There are two ways of making a digital image. Painting and drawing.
When you are painting, you lay down the pixels one by one like a tapestry.
When you are vector drawing, you click and drag, push and pull to make lines, shapes and fills that are created mathematically.
You can also draw freehand using the vector process. Adobe Ideas for iPad and iPhone is a good example of a vector drawing based art app.
Vector lines have the advantage of being sharp and smooth at any size. (Though they do have the disadvantage of sometimes being a bit too sharp and smooth.)
Digital painting and drawing are different experiences. Vector drawing with the push-me-pull-you method can feel more like sculpture than painting.
The object was to make as many faces as possible from just one circle and a line.
By duplicating, rotating and distorting two simple shapes, a circle and a line, you could make the eyes, ears and noses of all kinds of characters, and give them all kinds of expressions.
Duplicating and altering the size of the circle made the eyes and ears. Altering the line made expressions with mouth and eyebrows.
It isn't difficult to make a face. Almost any shape with two dots and a line in the right place can be seen as a face. In fact the earliest smileys didn't even have the two dots for eyes.
Creating facial expressions can be trickier. The tiniest alteration can completely alter an expression.