31-derful Puzzle
This blog post contains Amazon affiliate links. As an Amazon Associate, I earn a small commission from qualifying purchases.
31-derful is fun and easy-to-implement group problem solving activity that is a perfect activity for the first day or week of school. The only supplies needed to implement this activity is a deck of playing cards for each group.

I used the 31-derful activity with my Algebra 1 students for the first day of school. This year, I am emphasizing problem solving strategies and cooperative learning in my math classroom.
So, I chose first-day activities for my classes to participate in that would require or encourage them to work in a group. My Algebra 2 students completed an activity called Five Easy Pieces.
I learned about 31derful (pronounced thirty-wonderful) from Sarah Rubin at Everybody is a Genius. Her awesome pre-made graphics make it super easy to explain the rules of the puzzle to your students. I just put her images in my SmartBoard file.
Looking for more first day of school activities and puzzles for your classroom? I have a giant blog post dedicated to 40+ activities for the first week of school.
Here’s a few examples of some of these engaging activities for the beginning of the school year.
Supplies
Students are given a regular deck of 52 playing cards. If you have a casino near your school, you can sometimes get donations of playing cards for your classroom. You can also pick up playing cards in bulk from Amazon for relatively cheap.
Once you have playing cards in your classroom, you could also use them for activities such as the Pips Puzzle or the Playing Card Puzzle. They are also perfect for playing Sara VanderWerf’s 5 x 5 Game.
Instructions for Playing 31-derful
Their task is to choose 25 of those cards to arrange in a 5 x 5 pattern. Sounds easy enough, right?
The goal of the puzzle is to create rows and columns of cards that sum to exactly 31.
Each row and each column needs to add up to exactly 31. Often, students will get all the rows adding up to 31 before realizing that they were supposed to be paying attention to the columns, too!
The number cards have the same value as the number printed on them. Face cards are worth 10. Aces are worth 11.
My Experiences with 31-derful
One thing I’m going to definitely have to work on with my Algebra 1 students is listening and following directions. When I explained the rules to the game many of my students did not listen well or stopped listening after they thought they knew how the game went.
As a result, many of my students thought that only the rows had to add up to 31. They were a little mad after discovering that they weren’t actually done with the puzzle because their columns did not add up to 31 as well.
I was disappointed with how my students did with this activity. In my three Algebra 1 classes, only one group of students was able to successfully complete the puzzle.
A lot of my students decided that this puzzle was impossible.
They were quick to grow frustrated and give up. We’re definitely going to have to work on persevering in problem solving this year!
I did learn a very important lesson on this first day of school. They make special decks of cards to play pinochle. If you unintentionally give a group of students a deck of pinochle cards to play 31-derful with, they will get extremely frustrated.
You will wonder why they are only using 9s, 10s, Jacks, Queens, Kings, and Aces to build their array of cards. They will be wondering why those are they only cards you gave them.
Eventually, you will look at the box of cards and see that it is a pinochle deck. You will google pinochle and learn that a pinochle deck consists of eight each of the above cards.
Puzzle Solutions
Puzzle solutions are available on a password-protected solution page. I do not openly post the puzzle answer keys because one of my goals as a resource creator is to craft learning experiences for students that are non-google-able. I want teachers to be able to use these puzzles in their classrooms without the solutions being found easily on the Internet.
Please email me at sarah@mathequalslove.net for the password to the answer key database featuring all of my printable puzzles and math worksheets. I frequently have students emailing me for the answer key, so please specify in your email what school you teach at and what subjects you teach. If you do not provide these details, I will not be able to send you the password.
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, or as fun activities in their workplace. Just give me enough details so I know you are not a student looking for answers to the puzzle that was assigned as their homework!