Picasso Brush

A stroke is only as long as one end number divided by the other, so covering the paper is a hunt for factors.

The Picasso Brush board

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Grades
2–6
Subjects
Multiplying & Dividing
Kind
Puzzle
Cost
Free, no account, no ads
Original
Picasso’s Canvas at MathPickle

What it is

The canvas is numbered, and a brushstroke runs from one square to another. Its length is not yours to choose: it is the bigger of the two end numbers divided by the smaller. A stroke may never double back alongside its own paint, and the goal is to leave as few blank squares as you can.

The rules

Cover the numbered canvas with brushstrokes.

A brush starts on the number 3 of a numbered canvas and paints down it a square at a time. On the third square the number 12 beside it is ringed in green, and the stroke lands on it four squares long, because twelve divided by three is four.1234567891011121314151612345678910111213141516123456789101112131415161234567891011121314151612 ÷ 3 = 4
A stroke is as long as its bigger end ÷ smaller end.
A half-painted stroke has turned a corner. The free square inside the turn is hatched out, because painting it would put the brush back alongside its own paint; the square the other way is offered instead. The stroke takes it and runs on to finish.123456789101112131415161234567891011121314151612345678910111213141516
A stroke never runs back alongside its own paint.
A canvas with three strokes on it and 9 squares still blank. One more long stroke goes on, and only 1 square is left showing.123456789101112131415169123456789101112131415161
Leave as few blank squares as you can.

Drag from square to square, and let go to finish a stroke. Tap a stroke to wipe it.

Puzzles by Gordon Hamilton, MathPickle (2018).

What it gives you to practise

Division asked the useful way round. Nobody hands you 12 ÷ 4 and waits; you are looking at a canvas and asking which pairs of numbers divide cleanly enough to reach where you need to get to. Factors become something you hunt for rather than something you recite. And like Mondrian, it does not end — there is only a canvas with fewer blank squares than the one before it.

In a classroom

Gordon Hamilton, MathPickle, 2018. It pairs well with Mondrian Puzzle in one lesson: two boards that refuse to finish, one scored by a subtraction and the other by a division.

Share or embed

The whole puzzle at one address, with every board in it. Whoever opens it stays inside it, and their progress stays in their own browser.

Play Picasso Brush

Near it on the shelf