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Equal Sums Puzzle

Can you place the numbers 1 to 5 in the correct places to solve the equal sums puzzle?

equal sums puzzle.

Puzzle Instructions

Place the numbers 1 to 5 in the triangular diagram so that the sum of the numbers on the vertices of the smaller triangle is equal to the sum of the numbers on the vertices of the larger triangle.

Puzzle Source

I ran across this puzzle in a collection of 199 different mathematical puzzles that is offered as a free download from IREM de Lyon. This is a top-notch puzzle resource if you speak French.

I sadly do not speak French, but I was able to use the Google Translate app to translate quite a few of the puzzle instructions in order to use them in my classroom. Other puzzles I typed up from this same resource is the U Sums Puzzle, Magic H Puzzle, and Lines of 3 Puzzle.

This specific puzzle is #199 – Sommes sur triangles. This translates to “Sums over Triangles.” I have already shared another puzzle previously which I called Triangle Sums, so I decided to just call this one Equal Sums to avoid confusion.

Using the Puzzle in the Classroom

I recently used this Equal Sums puzzle as one of my Puzzles of the Week in my high school math classroom. This puzzle was definitely on the easier side for my high school students, so I made sure to pair it with a few of my trickier puzzles like the Equilateral Triangle Puzzle and the Eight Checkered L’s Puzzle.

equal sums puzzle as puzzle of the week.

I hang my weekly puzzles on the dry erase board in these fabulous magnetic pockets that I ordered from Charles Leonard on Amazon.

When students get to class, they often grab one of the puzzles off the dry erase board and take it to their desk to work on before class starts. Other students gravitate towards the puzzles when they finish early.

Since this puzzle is on the easier side, it would make a great warm-up activity or a brain break activity.

The only trouble my students had with this puzzle was their unfamiliarity with the word “vertices.” I had to answer so many questions about what that word meant over the course of the week.

Printing and Prepping the Puzzle

This puzzle is designed to print on letter-sized paper. I suggest printing the puzzle board on regular copy paper or cardstock and running it through a laminator to make the puzzle more durable.

Equal Sums Puzzle Screenshot.
Equal Sums Puzzle Pieces.

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.