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Tiles on a Patio

How many ways can you find of tiling the square patio, using square tiles of different sizes?


Age 7 to 11 Challenge Level:

If you are a teacher click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on ...

Picture of some squares

Nine squares with side lengths $1, 4, 7, 8, 9, 10, 14, 15$ and $18$ cm can be fitted together with no gaps and no overlaps, to form a rectangle.

What are the dimensions of the rectangle?


Once you've had a chance to think about it, click below to see how three different pupils began working on the task.


This is how Anna started:


Here is what Brendan tried:


Here is Chandra's initial approach to the problem:


Can you take each of these starting ideas and develop them into a solution?