Mondrian Puzzle

Every rectangle painted is a multiplication, and the score is the gap between the biggest one and the smallest.

The Mondrian Puzzle board

Play Mondrian Puzzle Share or embed

Grades
2–6
Subjects
Shapes & Space, Multiplying & Dividing, Adding & Subtracting
Kind
Puzzle
Cost
Free, no account, no ads
Original
Mondrian Art Puzzles at MathPickle

What it is

Cover the whole canvas with rectangles, no two of them the same shape — a 2×3 and a 3×2 count as the same shape, so only one of them may appear. Each rectangle says how many squares it covers, and your score is the biggest minus the smallest. Lower is better. There is no way to finish except by finding something better than your last answer.

The rules

Cover the whole canvas with rectangles, no two of them the same.

A finger drags down a blank canvas and a dashed rectangle grows under it. It lets go and the rectangle is painted, showing the ten squares it covers, and two more rectangles fill the rest of the canvas.4610101096
Drag corner to corner. A rectangle says how many squares it covers.
A painted canvas where one rectangle is two squares across and three down, and another is three across and two down. Both are hatched and their numbers turn red. They come off, and the left of the canvas is repainted as one tall rectangle, which the board accepts.4966491096
A 2×3 and a 3×2 are the same shape — you may use only one of them.
A finished canvas of three rectangles covering ten, nine and six squares. The biggest is ringed, then the smallest, and the sum ten take away six equals four is written underneath.109610 − 6 = 4
Score = biggest − smallest. Lower is better.

Tap a rectangle to take it off again.

What it gives you to practise

Every rectangle dragged out is a multiplication you have to do to know what you have made, and the score is a subtraction between two of them. The optimisation is the real content: there is no target to hit, only a number to push down, so a board stays open as long as somebody is still interested in it. For the larger canvases nobody knows the best possible score. That is not a puzzle withholding its answer key; it is an unsolved problem.

In a classroom

Gordon Hamilton designed it for exactly this — one board in front of a whole class, everybody pushing the same number down. Every legal answer found on the device is kept on a wall beside the board, sorted by score, so attempts accumulate instead of vanishing when somebody else has a go.

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 Mondrian Puzzle

Near it on the shelf