Nine Squares Puzzle
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Today I’m sharing a puzzle I’m calling Nine Squares Puzzle.
A few days ago, Shelli tweeted about needing more puzzles for next year since her advisory students will have already seen the ones she has used previously. This reminded me that I too will have this problem because my Pre-Calc classes will be made almost entirely of students I had this past year for Algebra 2.
I remembered seeing a puzzle I wanted to recreate a few weeks ago when I was typing up the Twelve Envelopes Puzzle that I plan on using for the first day of school. This was just the push I needed to type it up!
I picked up a copy of Giant Book of Hard-to-Solve Mind Puzzles about a month ago at Goodwill for two dollars. It’s out-of-print which makes used copies from Amazon VERY expensive.
If you happen upon a copy of this book at a thrift store or used book shop, it’s definitely worth picking a copy up, though!
The book calls this puzzle “Nine Circles,” but I’ve renamed it “Nine Squares Puzzle” because squares are much easier to cut out than circles!
The goal of the nine squares puzzle is to place the numbers 1 through 9 in the 9 provided squares so that the number in any square in the upper row is equal to the sum of the numbers in the two squares immediately below it.
For example, I could place a 6 in the top row and a 4 and 2 immediately below it since 4 + 2 = 6.
The nine squares puzzle is a trickier puzzle than it first seems. I thought I was on a roll with this next attempt at solving the puzzle. 9 = 5 + 4. 7 = 4 + 3. None of my remaining numbers were three apart, so I had to scrap this attempt and try again.
With a lot of perseverance and a bit of teamwork in puzzle solving from my husband, we succeeded in finding a solution. I’m not sure if there is a single solution or multiple solutions.
The book’s answer key might shed some light on this, but I try not to reference the answer section in a puzzle book because I always end up accidentally seeing the answer to another puzzle which I can’t unsee!
I’m excited about putting this nine squares puzzle out with my students to tackle. This year, I want to do a much better job at changing out my puzzles on a weekly basis. I typed up two slightly different versions of this puzzle to share.
The first version, as featured above, is meant to be solved on a table. My second version features larger squares and is meant to be solved simply using the squares without placing them on the outline on the puzzle board.
I will be attaching magnets to each of the nine squares and using them on my dry erase board.
The magnetic puzzles I did this past year included Double Letters, Equilateral Triangle Puzzle, Four Aces, and Matador Dominoes. My goal for this upcoming school year is to post one magnetic puzzle each week. This means I have a LOT of puzzle preparation to do this summer!
Digital Version
Cathy Gloade has been busy at work creating digital versions of a ton of activities. Check out her entire collection including some from other sources. Check out Cathy’s Google Slides version of the Nine Squares puzzle.
Jennifer Massey has also created and shared a Google Slides version of the Nine Squares Puzzle.
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 sarah@mathequalslove.net with information about what you teach and where you teach. I will be happy to forward an answer key to you.
Not a teacher? Go ahead and send me an email as well. Just let me know what you are using the puzzles for. I am continually in awe of how many people are using these puzzles with scouting groups, with senior adults battling dementia, as fun activities in their workplace, or as a birthday party escape room.
More Puzzles with Movable Pieces
- 2025 Square Edge Matching Puzzle
- 2025 Pentomino Puzzle
- 2025 Puzzle – Yearly Digit Grid Puzzle
- Snowflake Square Edge Matching Puzzle
- Christmas Fill-In Puzzle
- Kwanzaa Square Edge Matching Puzzle
- Hanukkah Square Edge Matching Puzzle
- Christmas Tree Square Edge Matching Puzzle
- 8 Queens Puzzle
- Pentominoes Truck Puzzle
- Hawai’i Square Edge Matching Puzzle
- Pentominoes Parrot Puzzle
I love these puzzles and use them with my middle schoolers. But since I like to know for sure that it's possible, I try to solve them before I give them out.
Spoilers ahead! I've only found one solution so far, and was curious if it was the same as Sarah's. I have in the top row 5, 7, 9, 8. Is that the same one you found, Sarah?
I have a slightly different solution. I have 9, 8, and 7 on the top row with a different number other than 5.
Thanks for the challenge. I gave it to to my students unsure whether there was an actual solution. I think I got the same solution as you, Sarah. I did realize that the sum of the top row must equal the sum of the two ends of the bottom row plus twice the sum of the middle three. So this led to me the solution that Brian Q was referring to. There may be others.
This is a great puzzle. I spent this afternoon committed to working until I found a solution and I was fortunate to eventually do so! I was curious how many solutions there might be, so I wrote a program that determined there to be exactly 6 unique solutions.
Dan, a buddy of mine did something similar. He found 6 solutions, but I believe 3 are mirror images of the others?
Can you please tell me the answer
8 9 7 5
2 6 3 4 1
hkms gang you're welcome my good sir