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Maximize the Sum Puzzle

Today I want to share the Maximize the Sum Puzzle with you.

My Algebra 1 classes managed to get a bit off schedule of one another this past week. So, I declared Monday to be a “Catch-Up Day.” My classes that were behind were given our latest assignment and the class period to work on it. My classes that were caught up worked on finishing the assignment they had already started and working on any other missing assignments.

Maximize the Sum Puzzle in Dry Erase Pocket

My classes that were ahead of my other classes were given the chance to “Maximize the Sum.” This is yet another puzzle that I found in Puzzle Box, Volume 3. Yes, I know I seem a bit obsessed with this series of puzzle books. I promise it is for good reason!

Students are given a grid of 25 numbers. Their task is to circle five numbers from the grid that will maximize the sum. There is a twist: no two numbers can be circled if they are in the same row or column. So, you will end up with one number in each row and one number in each column.

Maximize the Sum Puzzle in Dry Erase Pocket

My students had a hard time understanding these rules despite reading them (at least I think they read them!) and my going over the rules at least twice.

Maximize the Sum Puzzle in Dry Erase Pocket

I printed off the maximize the sum puzzles and slid them each into a dry erase pocket so that students could easily change their circled numbers after finding the sum.

If you don’t have a classroom set of dry erase pockets, you could also use heavy duty sheet protectors. But, I highly recommend investing in a classroom set of the pockets since they are so much more durable.

I had students yell out their sums as they found them, so that students would know what the “sum to beat” was. My students ended up coming up with a higher sum than the answer key at the back of the book said, so I’m pretty confident we maximized the sum.

When I solved the maximize the sum puzzle, I found it very interesting that my first and second approaches to the puzzle which I thought would maximize the sum actually didn’t! This puzzle didn’t take my students very long at all. We were completely done with the puzzle in less than five minutes. So, this one is great if you are short on time!

Free Download of Maximize the Sum Puzzle


Maximize the Sum (PDF) (765 downloads)


Maximize the Sum (Editable Publisher File ZIP) (153 downloads)

I can’t recommend checking out the Puzzle Box books enough for other puzzles to use in your classroom!

Want even more puzzles for your classroom? Check out my puzzles page!

Puzzle Solutions

I intentionally do not share solutions to the puzzles I feature on my website because I strive to provide learning experiences for my students that are not 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.