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Sankaku Puzzles

Sankaku puzzles are a geometric based logic puzzle that focuses on finding the area of a triangle. The goal of each puzzle is to connect three dots to form a triangle with the specified area.

sankaku puzzles

Sankaku puzzles are the creation of Naoki Inaba, a prolific Japanese puzzle creator. I first discovered these puzzles several years ago on Inaba’s website (which is written entirely in Japanese), and I featured them in a round-up on my blog of Japanese Logic Puzzles for the Secondary Math Classroom.

I recently ran across them again, and I decided that they deserved their own entire blog post to hopefully help them get the attention they deserve. These puzzles should be of special interest to geometry teachers or anyone who includes teaching about finding the area of triangles in their curriculum.

Sankaku Puzzle Example and Written Directions

Inaba includes 42 of these triangle-finding puzzles on his website. They are spread over eight pages which I find really hard to print and use in my math classroom as-is.

Screenshot of First Page of Sankaku Puzzle File

I decided to compile the puzzles into a Word document so that they only take four pages instead of the original eight. I also added my English translation of the original Japanese instructions.

I printed these four pages in booklet mode to make a mini puzzle book of the sankaku puzzles for my students.

Piece of paper folded in half with sankaku puzzles printed on it

As you can see inside the booklet, the puzzles start out on 3 x 3 grids, but they quickly increase in difficulty to 4 x 4 grids.

Inside of Sankaku Puzzle Booklet

I hope you and your students enjoy hunting for triangles as you solve these sankaku puzzles!

Example of Four Solved Sankaku Puzzles

If you like these puzzles, I highly suggest you check out Naoki Inaba’s other math-based logic puzzles. His Zukei Puzzles are another great puzzle for geometry teachers!

Puzzle Solutions

ANsWer key link

Puzzle solutions are available on a password-protected solution page. I do not openly post the puzzle answer keys because one of my goals as a resource creator is to craft learning experiences for students that are non-google-able. I want teachers to be able to use these puzzles in their classrooms without the solutions being found easily on the Internet.

Please email me at sarah@mathequalslove.net for the password to the answer key database featuring all of my printable puzzles and math worksheets. I frequently have students emailing me for the answer key, so please specify in your email what school you teach at and what subjects you teach. If you do not provide these details, I will not be able to send you the password.

Not a teacher? Go ahead and send me an email as well. Just let me know what you are using the puzzles for. I am continually in awe of how many people are using these puzzles with scouting groups, with senior adults battling dementia, or as fun activities in their workplace. Just give me enough details so I know you are not a student looking for answers to the puzzle that was assigned as their homework!

Sarah Carter teaches high school math in her hometown of Coweta, Oklahoma. She currently teaches AP Precalculus, AP Calculus AB, and Statistics. She is passionate about sharing creative and hands-on teaching ideas with math teachers around the world through her blog, Math = Love.

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