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Triangle Sums Puzzle

In the Triangle Sums Puzzle, you are challenged to arrange the numbers 1 to 9 in the squares so that the sum of the numbers in each pair of squares is the same as the number in the triangle that touches both squares in the pair. You may only put one number in each square, and you may use each number only once.

triangle sums puzzle

I found the Triangle Sums Puzzle in The Little Giant Encyclopedia of Puzzles by The Diagram Group. I am always on the lookout for new puzzles that I can use with my students from pretty much any puzzle book I can get my hands on.

I printed the triangle sums puzzle on 11 x 17 cardstock. Then I printed the numbers 1 through 9 on colored paper which I laminated and cut apart.


drawing of laminator machine with text "laminating recommendations"

A laminator is a MUST-HAVE for me as a math teacher! I spent my first six years as a teacher at a school with a broken laminator, so I had to find a way to laminate things myself.

I’ve had several laminators over the years. I currently use a Scotch laminator at home and a Swingline laminator at school.

I highly recommend splurging a bit on the actual laminator and buying the cheapest laminating pouches you can find!

I have also uploaded an 8.5 x 11 inch version if you don’t have the ability to print on larger paper sizes.

Triangle Sums Puzzle

I print on 11 x 17 at school by using the bypass tray on my school’s copy machine. This size of paper makes the perfect size for students to work on in small groups.

Triangle Sums Puzzle

I find it is much easier for students to not use a number more than once if they have movable pieces.

Here’s a partial (but incorrect) solution. 5+4=9. 4+8=12. 8+3=11. 3+6=9. The next number would be 2 since 6+2=8. However, the 2 needs a 4 to sum to 6, but 4 has already been used.

Triangle Sums Puzzle

Have fun puzzling with this puzzle on your own or with your students!

Free Download of Triangle Sums Puzzle

Triangle Sums Puzzle (11 x 17) (5560 downloads )

Triangle Sums Puzzle (8.5 x 11) (5929 downloads )

Looking for more free puzzles to use in your classroom? Check out my puzzles page!

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.