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Square the Shapes Puzzle

I’m very excited about the Square the Shapes Puzzle (this week’s puzzle table selection) because it’s got some hidden mathematics involved in solving it that aren’t obvious at first glance.

I find that my students are less likely to tackle the puzzle on the puzzle table when the math connection is blatantly obvious.

Square the Shapes Puzzle

This week’s puzzle is called “Square the Shapes.” It is found in The Big, Big, Big Book of Brainteasers by The Grabarchuk Family. Sadly, the book is now out of print and the copies on Amazon at the moment are more than a bit pricey.

You can still access quite a few of the puzzles for free, though. Amazon’s Look Inside Feature lets you look at quite a few of the puzzles in The Big, Big, Big Book of Brainteasers for free. Just keep clicking “Surprise Me!” on the left pane to see a different page of puzzles.

So, how does the square the shapes puzzle work? The puzzle board contains a grid of dots and one of each of the shapes involved in the puzzle: square, triangle, circle, and pentagon.

Square the Shapes Puzzle

You are given three additional circles, pentagons, triangles, and squares to place on the grid.

Square the Shapes Puzzle

Your task is to place the additional shapes on the grid so that a square is formed by each separate set of shapes. So, the four squares will form a square. The four triangles will form a different square.

The four pentagons will form a third square. And, the four circles will form a fourth square. To further complicate things, each square that is formed must be a DIFFERENT size.

This requirement for each square to be a different size has proved a challenge for my students who have tackled this puzzle so far this week.

I had to give one student a quick reminder lesson about finding the length of the hypotenuse of a 45-45-90 triangle, so this puzzle is definitely more geared towards older students.

Free Download of Square the Shapes Puzzle

Interested in trying this square the shapes puzzle yourself or with your students? The puzzle board and puzzle pieces are both designed to print on letter-sized paper. The puzzle pieces actually print 4 sets to a page.

Square the Shapes Puzzle Board (PDF) (1180 downloads )

Square the Shapes Puzzle Pieces (PDF) (1064 downloads )

Square the Shapes Puzzle (Editable Publisher File ZIP) (812 downloads )

Puzzle Solutions

I intentionally do not make answers to the printable math puzzles I share on my blog available online because I strive to provide learning experiences for my students that are non-google-able. I would like other teachers to be able to use these puzzles in their classrooms as well without the solutions being easily found on the Internet.

However, I do recognize that us teachers are busy people and sometimes need to quickly reference an answer key to see if a student has solved a puzzle correctly or to see if they have interpreted the instructions properly.

If you are a teacher who is using these puzzles in your classroom, please send me an email at with information about what you teach and where you teach. I will be happy to forward an answer key to you.

Savanna Bunch

Friday 14th of May 2021

She gave the clue up above with the 45-45-90. A diagonal is longer than a side, try rotating one of the squares you made.


Thursday 6th of June 2019

its impossible


Wednesday 28th of November 2018

I agree. Unless I am misunderstanding the question, one of the given shapes must be on an outside corner to form a 4 by 4 square.

Teach in Wentzville

Wednesday 21st of November 2018

Ww couldnt get 4 different sqaure shapes... Because you would need one shape on the outside right? None of the Students got this one.

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