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The yearly number challenge is a simple to explain puzzle that will keep you captivated for hours. Using the digits in the current year exactly one time each, can you write a mathematical expression for each digit between 1 and 100? You may use any mathematical symbol or operation of your choosing.

## What is the Yearly Number Challenge?

The goal of the challenge is to use the digits in the current year (2023) exactly one time each along with any mathematical symbol or operation of your choosing to create expressions equivalent to the numbers between 1 and 100.

## What Mathematical Symbols or Operations Are Allowed?

Concatenation

- You are allowed to join digits together to form larger numbers. For example, 2 and 0 can be concatenated to form 20. 2 and 3 can be concatenated to form 23 or 32.

Decimal Points

- Decimal points may be placed between digits such as 2.0 or 2.2.

Basic Arithmetic Operations

- Addition
- Subtraction
- Multiplication
- Division

Grouping Symbols

- Parentheses
- Brackets
- Braces

Exponents/Radicals

- If you choose to use an exponent, it must be one of the digits in the year. Additionally, it counts as your use of that digit. For example, in the 2023 challenge, you could use 3^2 +20 for 29.
- Square roots are allowed. This does not count as the use of the digit 2.

Other Math Symbols

- Factorials – I like to use this activity as a way to introduce my students to the concept of factorials. The factorial of a number is the product of all positive integers less than or to the number.
- 0! = 1 [
**THIS FACT COMES IN VERY HANDY WITH THIS CHALLENGE!**] - 1! = 1
- 2! = 2 * 1 = 2
- 3! = 3 * 2 * 1 = 6
- 4! = 4 * 3 * 2 * 1 = 24
- 5! = 5 * 4 * 3 * 2 * 1 = 120

- 0! = 1 [
- Double Factorials – Double factorials are related to factorials, but they involve multiplying by only the numbers that have the same parity (even or odd) as the original number. [
**NOTE: Desmos does not evaluate double factorials. It simply applies the factorial function twice.**]- 4!! = 4 * 2 = 8
- 5!! = 5 * 3 * 1 = 15
- 6!! = 6 * 4 * 2 = 48

- In need of a review of how factorials work? I created a free printable factorials table that both reviews the concepts of factorial and double factorial and provides a handy chart of factorial values to reference.
- I also created a free printable factorials poster that you can print and hang in your classroom for students to reference.
- I have seen some people use the floor and ceiling functions in this challenge, but I have never allowed my students or myself to do this. It has always seemed too much like “cheating” to me.

**Ultimately, remember that this challenge can be whatever you need it to be. Feel free to change the rules to meet your students’ needs! **

## Extra Challenge

Want even more of a challenge? How many numbers can you find if you keep the digits in order each time?

## How Can I Use this Challenge in my Classroom?

I have been using the yearly number challenge in my classroom in various forms since 2016. Over the years, the challenge has taken various forms. In 2019, I turned the yearly number challenge into a group competition.

For several years (2016-2018), I formatted the yearly number challenge as a free printable bulletin board. Most recently, I have been making a printable challenge sheet with spaces for students to write in each solution as it is found.

**WARNING**

Some year’s challenges are easier to solve than others. **Make sure students realize that they may not be able to find all of the solutions!**

## 2023 Challenge

When I use the yearly number challenge with my high school math students, I challenge them to find mathematical expressions for as many of the numbers between 1 and 100 as possible. I have created a free printable sheet for them to fill out as they find solutions for various numbers.

Some years it is possible to find more numbers in the challenge than other years.

Depending on the age and math ability of your students as well as the amount of class time you would like to dedicate to this activity, you may wish to only have your students find a subset of the numbers.

This year, I ended up creating 6 different versions of the 2023 Challenge that you can print and use with your students. Challenge your students to find the numbers 1-10, 1-20, 1-30, 1-40, 1-50, or 1-100 using the digits in 2023.

I would suggest printing off the challenge sheet with all 100 numbers on it and then try to find as many solutions as possible using the type of mathematical operations that you expect your students to use while solving. Once you see how many you are able to solve on your own, you can then decide which level of challenge will be appropriate to your students.

1-100 Challenge

1-50 Challenge

1-40 Challenge

1-30 Challenge

1-20 Challenge

1-10 Challenge

If you are looking for another way to celebrate the new year, check out my 2023 puzzle!

### Free Download of 2023 Challenge Worksheet

2023 Challenge (PDF) (4397 downloads)

2023 Challenge (Editable Publisher File ZIP) (1223 downloads)

### Digital Version of 2023 Challenge

Craig Winske has created a Desmos version of the 2023 Challenge.

## Previous Year’s Challenges

### 2022 Challenge

Today was the first day of the new semester. I issued my students the 2022 Challenge to get their brains re-engaged in doing math without having to jump straight into content on day one.

What is the 2022 Challenge?

The goal of the challenge is to use the digits in 2022 (2, 0, 2, and 2) exactly one time each along with any mathematical symbol or operation of your choosing to create expressions equivalent to the numbers between 1 and 100.

I first learned of this type of yearly number challenge in 2016. I first started by creating large posters that could be hung on a bulletin board with the challenge on them for students to fill in. In 2019, I changed things up and did a group competition for the 2019 Challenge.

In 2020, I decided that only having two two’s and two zero’s was a bit too restrictive, so I didn’t end up doing the 2020 Challenge with students. We started off the 2021 school year with students learning remotely, so the 2021 Challenge didn’t happen either.

This year, I wasn’t sure exactly how much of the 2022 Challenge that my students would be able to complete, but I decided to give it a shot anyway. I also decided to change things up this year and do the yearly number challenge as a worksheet.

I actually kicked off class with an ACT question featuring factorials. The majority of my students have never encountered factorials before, and I knew that we would have much more success with the challenge if we were able to capitalize on the fact that 0! = 1.

We worked through the ACT problem, I taught them the word “factorial,” and then I challenged them to use their new understanding of factorials to determine the value of 0!.

After revealing that 0! is 1, I told them that this fact might come in handy today and handed out the 2022 Challenge worksheet.

At this point, we discussed the directions. I intentionally left the directions vague since I find that it’s best for students to get started on the challenge and then let them start asking questions.

This is when I tell them that concatenation (for example joining 2 and 0 to form 20) is allowed. I also give them ideas of different mathematical symbols they can use like parentheses, decimal points, factorial, and exponents.

The caveat with exponents is that the exponent has counts as one of the digits. Some students also get it in their heads that they need to keep the digits 2, 0, 2, and 2 in that order.

NCTM calls this the “Year Game” and encourages students to keep the digits in the original order whenever possible. I thought that this year’s challenge was hard enough without encouraging this restriction.

To give my students a bit of extra motivation to engage with the activity on the first day back from break, I decided to pit my classes against one another in a contest. I told them whichever class period found the most solutions to the challenge would win cookies.

Apparently, teenagers love food because I found that my students were engaged and quite competitive. My afternoon class even went as far as to compile all of their results on the dry erase board to make sure that students weren’t working on numbers that had already been solved by another group.

They also argued that their class was at a disadvantage since they had half as many students as some of my other classes. They wanted me to change the rules to make it ratio based, instead.

How many of the solutions ended up being actually possible to find? My students managed to find solutions to 45 different numbers between 1 and 100.

The numbers 1-10 are all possible. So, if you wanted to use this activity as a class warm-up you could challenge students to find expressions for the first ten numbers.

The solutions get quite scarce after 50. So, you might also want to edit the challenge to find only the numbers 1 through 50.

I know that you can use the floor and ceiling functions to find many more solutions, but this approach has always felt a little like “cheating” to me. So, I’ve never told my students about the floor and ceiling functions as an option.

I’m looking forward to hearing how many solutions your students find!

#### Free Download of 2022 Challenge Worksheet

2022 Challenge Worksheet (PDF) (6627 downloads)

2022 Challenge Worksheet (Editable Publisher File ZIP) (2132 downloads)

### 2019 Challenge

Even though it’s now the middle of summer, I’m just now getting around to blogging about an activity that we did in January. Yes, that pretty much sums up how this year’s blogging is going. I feel like almost every post starts with an apology of how late the post is.

So, without further apology, I want to share with you the 2019 Challenge. We’ve still got a few months of 2019 left, so I guess the post isn’t too tardy yet.

Kicking off the spring semester with a challenge based on the new calendar year has become a bit of a tradition in my classroom. Let’s take a bit of a trip down memory lane.

I fully had plans to put up the 2019 Challenge as a bulletin board before we went on Christmas Break. That did not happen. Then, our first day back from Christmas was cancelled due to ice.

This meant our normal two-day week to welcome us back to the second semester was now a one-day week. There was no way that I was starting new content on a one-day week, so I decided to take the 2019 Challenge I had planned to put up as a sort of puzzle for early finishers and turn it into an entire class activity.

Note: I usually use this as a “Welcome to the new semester!” activity, but you could just as easily use this as a “Welcome to the new school year!” activity in August/September.

If you’re not familiar with the challenge, the goal is to use the digits in 2019 (2, 0, 1, and 9) exactly one time each along with any mathematical symbol or operation of your choosing to create expressions equivalent to the numbers between 1 and 100.

I gave them a list of some of the possible mathematical operators to get their brains moving.

I love to use this challenge to introduce students to one of my favorite words: concatenation.

Concatenation means that 2 and 0 can be combined to make the number 20.

My students have yet to be introduced the concept of factorial yet, so I gave a quick tutorial on what it looks like and what it means. We started by trying to complete this chart.

We started by trying to complete this chart as a class on the dry erase board. It was interesting to hear students’ theories evolve as each new answer was revealed.

In the past, I would post the challenge, introduce it to my students, and let them fill out as many solutions as possible. As the first day would progress, the challenge would get more and more difficult as the easier numbers that could be achieved by simple addition and subtraction with maybe a little multiplication thrown in were already claimed.

I needed to keep six entire classes of students engaged, so I decided to have each class start the challenge from the beginning. That’s when I got the idea to pull out my 100 number chart that I purchased last year from Amazon.

Then, I spent some quality time with the paper chopper and some cardstock to cut out a different colored set of squares for each of the six groups that my desks are arranged in. I sized these squares to be the same size as the 1-100 cards that fit in my 100 number chart.

Groups would work together to find as many expressions as possible to equal numbers between 1 and 100. When a group found an expression for an unclaimed number, they would bring their solution up to get it verified.

If it was correct, they would place one of their squares of cardstock on top of the number to “claim” it for their team.

By the end of the 50 minute period, the board would look something like this:

In some ways, this activity structure was better than my bulletin boards of the past. And, it also left some attributes to be desired. Let me try to reflect.

Adjusting this to a group-based competition did have some unintended consequences.

Some groups were WAY more hyper-competitive than I expected.

One group had one of their team members permanently stand next to the 100 number chart so that as soon as they figured out a number and got their solution checked they could mark it with the color for their team. This meant that this student was not doing any math at all which was not my intention.

I attempted to combat this by requiring in another class period that only one person from each group was allowed out of their seat. This solved the prior issue but created another.

One student from the group would tend to spend the entire time running answers up to my desk and getting them checked before marking off their numbers on the chart. This meant that there was still a student who was primarily doing no math at all.

Still yet another downside to the competitive team nature of this activity was that some groups tended to give up entirely as they realized JUST how far they were behind the other teams.

Some students started trying to play games on their phones instead of participating in the activity because they knew that their group was NOT going to win.

To combat this in the future, I might have students remove the cards from the chart after solving them and have them place them in a small box or basket for each team.

This way, everyone can still see what numbers remain unsolved, but they can’t easily see how far ahead or behind they are from the other teams.

I really appreciated the fact that making this into a group activity ended up engaging a vastly larger percentage of my students than my previous use of the activity with early finishers.

However, a trade-off was that my students weren’t necessarily learning from one another as much as they have in the past. This was because previously, students would write their solutions to each number on the bulletin board.

Often, students would take a solution for one number and end up tweaking it slightly to create a different number. Usually, this would involve adding a factorial symbol to a 0 to produce a 1 or something similar to that.

Frequently, students would see a solution written on the board and ask a question about it, thinking it was incorrect. This made a great teaching moment.

If I do this again, I might write 1-100 on the dry erase board and have students write their solutions next to each number as a step in the process. This keeps the competitive aspect while still encouraging students to learn from one another. It’s also easily erasable between classes.

I’ve got lots to think about before I decide how I want to proceed with the 2020 Challenge. My main concern isn’t the structure of the activity but what to do about the fact that we only have two 2’s and two 0’s to use. If you have any ideas, I’d love to hear them!

I’ll close this rather long rambly blog post with one of my favorite solutions to the 2019 Challenge.

#### Free Download of Poster/Bulletin Board Version of 2019 Challenge

2019 Challenge (PDF) (546 downloads)

2019 Challenge (Editable Publisher File ZIP) (528 downloads)

Yearly Challenge Bulletin Board Pieces (PDF) (1015 downloads)

Yearly Challenge Bulletin Board Pieces (Editable Publisher File ZIP) (676 downloads)

### 2018 Challenge

Tomorrow will be our first day back. It is a Professional Day, so I won’t see my students until Friday. I’m not exactly sure how I feel about only having a one-day week with kids, but I guess we’ll see how it goes.

I am looking forward to the chance to kick off one of my annual traditions – the 2018 Challenge. It’s a yearly task where students have to use the digits in the current year’s date to make each number between one and one hundred. For example, 28 + 10 = 38. Or, 28 + 1 + 0! = 30.

You can read about how I approached this challenge in previous years in my 2016 Challenge post and 2017 Challenge post. I originally learned about this task from Jeremy Denton who learned of the challenge from Mr. Collins.

Each year, I print off my challenge on 11 x 17 cardstock.

Last year, I used magnets to hang the challenge on my dry erase board.

My projector is dying and unreliable, so my dry erase board is prime real estate in my classroom at the moment. So, I decided to go back to using my bulletin board again this year.

I used my normal 11 x 17 templates that have spaces to write a solution and the name of the person that came up with the solution next to each number. I just had to update the instructions to say use the digits 2, 0, 1, and 8 instead of 2, 0, 1, and 7.

I decided to add visual reminders of which operations are allowed to spice up my bulletin board a bit.

Here’s a close-up of the instructions:

Want to join in with your own students? I’ve uploaded the files below. They are formatted to print on 11 x 17 cardstock. If you only have access to letter-sized paper, you can print them poster-style through Adobe.

Click on “Poster.” Then scale to 95% with a .001″ overlap. This will let you print the entire bulletin board set on letter sized paper. You’ll just have a bit more assembly to do!

Happy 2018!

### 2017 Challenge

I am super excited for 2017 because it means it’s time for a new yearly number challenge – the “2017 Challenge.”

I designed a template that would print on 11 x 17 cardstock — my go-to paper for making awesome classroom posters and displays!

I put up this bulletin board last year for the 2016 Challenge:

I’ve edited the files for 2017 instead of 2016. I also changed the font to my current obsession, Wellfleet!

For each integer between 1 and 100, inclusive, there is a space for students to write the solution. There is also a space to the right for students to write their name to show who found the solution.

ALL solutions must be verified by me before being added to the posters!

The last page in the file includes the instructions. Students are asked to create each integer between 1 and 100 using only the digits in 2017. Repeating digits is not allowed. Students may use any mathematical symbol or operation.

One thing I love about this challenge is it encourages students to learn about factorials which they haven’t had much exposure to at all.

Last year, it was fun to watch students work through this challenge. We did not complete it last year, but it is not always possible to find solutions to each number. The number of solutions that are possible depends on the year!

#### Free Download of 2017 Yearly Number Challenge

2017 Challenge (PDF) (489 downloads)

2017 Challenge (Editable Publisher File ZIP) (494 downloads)

Looking for another challenge? I highly recommend that you also check out the 5-4-3-2-1 challenge!

### 2016 Challenge

I’m excited introduce my students to a yearly number challenge based on the digits in 2016. You can play along with the digits of the year you are currently living in if you are reading this in the future.

New semester means new changes in my classroom. Let’s just say this change has some of my students excited and some of my students annoyed. Excited about a new challenge. Annoyed at the fact that the sticky note board is no more.

After a semester of students putting a sticky note (with their name on it) on the board each time they made a perfect score the first time on a quiz, I had a bulletin board with a BUNCH of sticky notes.

One good thing about having student aides? I didn’t have to take all of these down myself!!!

So, what’s gone up in its place?

The 2016 Challenge. Because, it’s…you know…2016. The goal is for students to create the numbers 1-100 using only the digits 2, 0, 1, and 6. Students may add/subtract/multiply/divide, use parentheses, exponents, factorials, square roots, or whatever their little heart desires.

I first learned about the challenge from Jeremy Denton on twitter:

A comment on that tweet led me to this blog post by Mr. Collins about the 2015 challenge.

I, of course, had to type up my own version to fit on American sized paper. My mom bought me a package of 11 x 17 cardstock a while back that I have put to good use in my classroom.

I decided that printing the challenge on this larger paper would save my sanity when it came to hang it up.

Here’s what the 2016 Challenge Bulletin Board ended up looking like:

Each number has a space to write the equation and a space for the student who found the solution to sign their name.

Here are the instructions for the Yearly Number Challenge. Create each number using the digits 2, 0, 1, and 6 (or the digits of the current year if you are reading this from the future). Repeating digits is not allowed. You may use any mathematical symbol or operation. Tip: 0! = 1.

So, it’s been one day. And, I’m super impressed by the response I’ve gotten from my kiddos. Let’s just say I’m not used to seeing kids huddled around my bulletin boards with their calculators having heated discussions. I could get used to this!

Here’s the results thus far:

The first page has been almost all filled in. The other pages still have a while to go. But, that’s a good thing. I know the progress will be MUCH slower from now on.

#### Free Download of Yearly Number Challenge – 2016 Challenge

2016 Challenge (PDF) (526 downloads)

2016 Challenge (Editable Publisher File ZIP) (505 downloads)

For the Publisher file, you’ll need this free font: HVD Comic Serif Pro.

## 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.

## More Number Based Challenges and Puzzles

- Fives Challenge Puzzle
- 3-1-4 Pi Day Number Challenge
- Fours Challenge Puzzle
- 2023 Challenge: Yearly Number Challenge
- Threes Challenge
- Twos Challenge
- 7 Free Printable Math Challenges to Enjoy
- Twosday Challenge Activity
- Strimko Puzzles in the Classroom
- Rotated Square Puzzle
- Make 30 Puzzles
- Which Side of the Line Numbers Puzzle