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Is it Possible Divisibility Puzzle

I’m making the most of the $2 I spent on this recent Goodwill find. The Giant Book of Hard-to-Solve Mind Puzzles is 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 up a copy! The Is It Possible Divisibility Rules Puzzle is the third puzzle I’ve created for my classroom based on this book.

I’ve already shared the 12 Envelopes Puzzle and 9 Squares Puzzle which also came from this book.

When I ran across this divisibility rules puzzle, I knew that it would make a lovely magnetic puzzle to post on my dry erase board for the upcoming year. I’m making it my goal to post a new puzzle on the board each week.

I don’t have space for a puzzle table like I had in the past at my old school (that’s what happens when you have 30 students crammed into a classroom), so I’ve found that the best way to engage students in puzzles is to make them vertical by posting them on the dry erase board.

The board is magnetic, and I’ve found I get the most engagement from students when the puzzles involve magnetic pieces that can be manipulated.

Here’s the task. Is it possible to use the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 to construct a ten-digit number divisible (without a remainder) by all the numbers from 2 to 18?

Is It Possible Divisibility Puzzle

I plan on putting disc magnets on the back of each digit. My magnets are currently locked away in my classroom, so that will probably have to wait until August.

Divisibility Rules Chart

If your students need a reminder of basic divisibility rules, I have a printable divisibility rules chart that can be used as a reference.

divisibility rules printable chart pdf.

Free Download of Is It Possible Divisibility Rules Puzzle

Want to play along at home or with your own students?

Is It Possible Divisibility Puzzle (PDF) (2126 downloads )

Is It Possible Divisibility Puzzle (Editable Publisher File ZIP) (995 downloads )

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.


Tuesday 23rd of July 2019

Hi Sarah, I know you don't post puzzle answers, but would you be able to tell me if this problem is possible to solve? I need to know whether it is possible before I give the problem to my students to solve. It's frustrating if they tried for over an hour and the answer is impossible. I don't want to buy the book, it's way to expensive. Thank you.

Sarah Carter (@mathequalslove)

Wednesday 24th of July 2019

Hi Bailey! It's definitely possible. There are a few spoilers posted on Twitter :)

Eva Zussman

Sunday 14th of July 2019

Hi. I love your blog and have been following for years. I would like to incorporate more of these puzzles into my classroom besides the first week of school. I don't think I've seen a blog post about how you actually use them in class. I know you used to have the puzzle table but when could students work on them? I don't really have extra space in my classroom and I feel like there is never any down time, but I think that my students would love these and it would really help them exercise their brains. Would you be willing to elaborate on how and when you let students work on these puzzles?

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