Magic Triangle: Math Puzzle for Kids

Are you ready to give your kids a fun math puzzle and brain teaser to streeeaaaatch their brains? I’m ready to give you one! Have you ever heard of the magic triangle puzzle? The concept is similar to the magic square, which was part of our diy Camp Mathematics last year. In that case, the numbers were arranged in a grid, but here the kids will be working on the triangle’s perimeter.

Both my 7 year old and my 11 year old really enjoyed trying to solve the puzzler. My 11 year old found the smaller triangle to be a breeze but the larger one turned out to be the perfect challenge. My younger son persevered through several errors, but was so proud of himself when he figured it out!

Enough delay. Let’s get started!

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There are several different kinds of magic triangles and I am sharing 2 of them with you. The great part, is that each puzzle has several solutions so the fun can last and last, and last…. and you can choose a puzzle based on your child’s age and abilities.

What you need:

• A kid! (one or more will do)
• Our printable! Download the printable here. (Note: by downloading you agree to our terms of service*)

OR

• Make your own with pencil and paper. The number counters I created are not strictly necessary, but it is easier to correct mistakes by moving the counters than by constantly erasing.

Instructions:

Arrange the numbers for each triangle (1-6 for the 3 x 3 x 3 triangle; 1-9 for the 4 x 4 x 4 triangle) so that the sum of numbers on each side is equal to the sum of numbers on every other side.

For the small triangle, arrange the numbers so that the sum of each side equals 9. There are also solutions for 10, 11 and 12.

For the large triangle arrange the numbers so that the sum of each side equals 17. You can also find solutions for 19, 20, 21, and 23.

Watch the video to see the magic triangle in action:

Extensions:

For advanced young mathematicians, do not tell kids what the sum for each magic triangle side will be. Simply give the instruction to arrange the numbers so that the sum on each side is equal to the others. Let them try and figure out that each side should add up to 9, for example.

This puzzle can be done with even larger triangles — with 5 numbers, or 6 numbers on each side. (You’ll have to make your own game board, however!) Can you figure out what the numbers on each side should add up to?

Want more triangle fun? Math Geek Mama has a printable so kids can explore patterns in Pascal’s Triangle.

About magic triangles:

I first learned about the magic triangle in my son’s book, See Inside Math (affiliate link). Upon further investigation I learned that perimeter magic was first written about by mathematician Terrel Trotter, Jr. It quickly became part of many a recreational math repertoire. You can learn more about the math behind the triangles on this website.

Why do this puzzle? 

Solving magic triangles exercises kids’ basic addition skills, but also critical thinking, mental math and logical thinking.

More fun math puzzlers:

• Math cubic riddle 
• Impossible paper puzzle
• T puzzle
• Pentalpha puzzle
• Colorku
• Sumoku

Solution:

I always strongly encourage you not to look at the solution? Can’t solve the magic triangle today? Try again tomorrow. Your kids will learn that it is MUCH more satisfying to solve a problem on their own, than to “cheat.” Nevertheless, I always get the question, “where is the solution??” So I’ll let you in on a secret: watch the video above and I reveal the solution at the end for all sums.

See more of our favorite math games in action:

*This printable is for personal or educational use only. Commercial use is prohibited. You may print out as many copies as you like. If you wish to share it with others, you must link to this blog post, not the pdf file directly.

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