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

What length are the sides of the rectangle?


Once you've had a chance to think about it, you may like to see how three different students began working on the task.


I came across this only the other day, lovely website! I let my subconscious work on this the past 24 hours, and found the solution.

If you'd like to see some hints about the methods I used, click below:

Approach was finding total area, doing prime factors on that, and thinking about possible rectangles. Of the 3 possible ones which can even fit an 18x18 square, only 1 would actually leave enough space for others to also fit in.

Lovely little puzzle, thanks!

Thank you for your comment, Nikki. I hope you don't mind that I've hidden your method under a 'Reveal' button so that we do not spoil anything for those who would prefer not to know, or not to know yet!