Favorite Simple Math Games: Pico, Ferme, Bagel

Do you need a logic-focused warm-up for math class? Are you looking for a no-prep activity to keep learning alive during dismissal? Look no further. Simple math games, such as Pico, Ferme, Bagel, are the perfect addition to your day.

Today, we’ll do a deep dive into the classic number game: Pico, Fermi, Bagel. This simple math game, also known as Pico, Fermi, Nada, requires zero prep and can be played almost anywhere.

In this post, I’ll share how to play, the history behind the game, the skills students will develop, and how I incorporated it into my packed schedule. Let’s go!

What is it?

Pico, Fermi, Bagel is a classic simple math game that challenges students’ logical reasoning and deduction skills. Even more, it boosts critical thinking about numbers without emphasis on specific operations (addition, subtraction, division, or multiplication). It can be tailored to all abilities but still works on key thinking strategies. Therefore, it sneaks extra math thinking into the day.

The game is similar to classic games such as Mastermind (one of my favorites as a kid) and, more recently, Wordle (one of my favorites as an adult).

Like Mastermind and Wordle, Pico, Fermi, Bagel involves guessing a secret sequence– this time, a sequence of numbers. The secret number is typically three digits long, with each digit being unique and ranging from 0 to 9. However, you can differentiate based on age, grade, and familiarity.

How to Play

Pico, Fermi, Bagel can be played in a small or large group. You just need to make sure there are at least two people: a code maker and a guesser. In my classrooms, I typically played in a whole group. I used it as a collaborative warm-up for the day. Alternatively, I occasionally used it as an extension activity in small groups.

Set-Up:

There are many ways and modes to play a simple math game such as Pico, Fermi, and Bagel. However, my favorite way to play is on a whiteboard with the whole class present.

Choose one player as the “code maker.” That one player, the “code maker,” creates a secret number combination. The code maker writes the number down on a slip of paper. This is key! Sometimes, the code maker forgets the original sequences. Guilty!

Note: You can also play with pen and paper. Or you can play it online here. My students loved to play it during travel on field trips, along with tic tac toe and the box game!

Here’s how to play:

Once the code is set, the other players make their guesses. With each guess, the code maker provides feedback using the terms “Pico,” “Fermi,” and “Bagel.” Each word has a special meaning.

• Fermi is the term used when a guessed digit is correct and in the correct position. For example, if the secret number is 459 and the guess is 430, the response would include “Fermi” for the number 4.
• Pico is the term that means a guessed digit is correct but in the wrong position. For example, if the guess was 274, and the secret number was 427, the code maker would respond with “Pico” for the digits 2 and 7.
• Bagel is the term that indicates that none of the guessed digits are in the secret number. A guess that shares no digits with the target number will earn this response.

The other players take turns making guesses. The code maker provides feedback using these terms. Usually, the code maker writes down the feedback. For example, if the guess is correct, the code maker would write “fermi, fermi, fermi” or “FFF.”

Concepts & Skills

Sometimes, even when we know a game has value, we still need to justify playing it. And those who have followed me for a while know that mathematical reasoning and critical thinking skills are my bread and butter. That’s why I’m obsessed with logic puzzles.

However, there is nothing fluffy about Pico, Fermi, Bagel. Sure, it is a simple math game. But it is all about critical thinking skills and logical reasoning.

At its core, the game challenges students to decipher a secret number by interpreting the feedback after each guess. Students must:

• Hypothesize
• Test
• Refine guesses

The game requires players to use inductive and deductive reasoning.

• Inductive reasoning comes into play as players form general rules about which numbers might be correct based on patterns observed from feedback.
• Deductive reasoning, on the other hand, comes into play when players eliminate possibilities. One by one, they narrow down potential solutions.

Additionally, Pico, Fermi, Bagel builds critical thinking. The rules require players to process and respond to information efficiently.

Like solving a mystery or logic puzzles, each response—whether it be “Pico,” “Fermi,” or “Bagel”—provides a new clue. Players must analyze those clues. It’s time to be strategic!

Talk about mental agility and adaptability!

Finally, Pico, Fermi, Bagel is the perfect low-stakes game to cultivate patience and perseverance. Players learn to persist through trial and error. They have to accept and reflect on unsuccessful attempts. Since the game is collaborative (except for the code maker), students who need support with perseverance thrive!

History of this Simple Math Game

If you’ve made it this far into the post, you might be wondering where did this game come from? If you are, you’re not alone. I was also very curious about the origins of this not-so-simple math game.

And it’s not-so-simple.

According to Desmos Classroom, in the 1980s, math legend Marilyn Burns published a version of the game in her book Math for Smarty Pants. However, numerous sources suggest that the game dates back (at least) to the 1970s. And, in a not-so-simple math game fashion, it has been recreated over and over again under many different names.

Extra Tips for the Classroom

The power of a simple math game is that there are endless ways to differentiate it. Pico, Fermi, Bagel is not an exception to that rule.

Simplify the Game

1. Shorten the Sequence Length: You can use two digits instead of a three-digit number. This limits the number of possible combinations and makes it easier for beginners to deduce the correct sequence.
2. Provide Initial Hints: Offer the guessers some initial hints. For example, you can reveal one correct digit without indicating its position. This can give them a starting point and make the game more accessible.
3. Allow Repeated Digits: Repetition of numbers reduces complexity.
4. Writing Down Clues: Finally, a great way to simplify this game is by allowing the code maker to write down the clues. This lifts some cognitive load off of the guesses.

Increase the Difficulty

Often, the best way to increase difficulty is similar to how I’d increase or decrease difficulty with logic puzzles. Since it isn’t about practice with operations, this game becomes more challenging by adding in more obstacles to the main goal: figuring out the mystery number.

1. Increase the number of digits: Extend the sequence to four or more digits. By doing this, you significantly increase the number of potential combinations. This makes deduction more challenging. Yikes!
2. Limit the Number of Guesses: A limited number of attempts forces the guessers to think more strategically about each guess. They can’t waste a single guess!
3. Change the Feedback: Who says it needs to be Pico, Fermi, Bagel? Try using symbols, colors or math manipulatives. Guessers can work double time to guess the clues and the clue system.

Do you need one more extreme challenge to add to Pico, Fermi, Nada? The University of Washington has you covered. In this exercise, players are challenged to think about the underlying logic of the game. Their worksheet asks:

What is the minimum number of guesses needed that will allow you to always
determine a secret number:
Where the secret number has one digit?
Where the secret number has two digits?
Where the secret number has three digits?

Can you find the answer?

Whether you call it “Pico, Fermi, Bagel,” “Pico, Fermi, Nada” or “Guess My Number,” your students will have so much fun playing. They won’t even realize they are building strong critical thinking and logical reasoning skills. I’d love to hear about your experience with this game. Have you played it as Pico, Fermi, Bagel? Share your thoughts in the comments!

Looking for other favorite games like this? Another favorite is “Digit Place: A Place Value Game!” Be sure to check it out!