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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 Puzzle Example and Written Directions

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.

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

I intentionally do not share solutions to the puzzles I feature on my website because I strive to provide learning experiences for my students that are not 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.