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Lines of 3 Puzzle

Can you place the numbers 1 to 7 in the diagram so that each line of numbers has the same sum?

lines of 3 number puzzle.

My students tackled this puzzle this past week as one of our puzzles of the week. A few of my high school students had a bit of trouble making sense of the puzzle directions. They just wanted to make just the two horizontal lines have the same sum.

So if you are working with younger students, it might be worth it to go over the directions before starting and make sure students realize where all of the lines of 3 are in the puzzle diagram.

Puzzle Instructions

Place the numbers 1 to 7 in the triangular diagram so that the sum of the numbers on each line of three circles has the same sum. One of the numbers (1) has already been placed.

lines of 3 puzzle screenshot.

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 Equal Sums Puzzle.

This specific puzzle is #192 – Alignement de trois jetons. IREM de Lyon credits the Tournai de St Michel en l’Herm (1990) for the original puzzle.

Printing and Prepping the Puzzle

I printed the puzzle boards on plain letter-sized paper and ran them through the laminator.

lines of 3 puzzle.

I used some of my colorful Astrobrights paper to print the page of circular number pieces. I also ran these through the laminator.

Note: One page of number tiles is enough for four separate copies of the puzzle. Please plan your printing accordingly.

lines of 3 puzzle pieces.

You could also skip the circular number tiles and have students write the numbers in directly on the puzzle. You could do this either by sliding the puzzle in a dry erase pocket and having students write with dry erase markers or by printing it as a math puzzle worksheet.

lines of 3 puzzle in notebook.

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.

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