Last One Standing
How it works
There are a bunch of people standing in a circle. People are eliminated one at a time as follows:
- Person #1 is skipped, then person #2 is eliminated.
- Next, person #3 is skipped, then person #4 is eliminated.
- We continue like this, skipping one person then eliminating the next person (ignoring any people who have already been eliminated) until there is only one person left. This person is the last one standing.
If your goal is to be the last one standing, which person should you be? Does your answer depend on the number of people?
In this activity, students explore which person is the last one standing for different numbers of people. Their goal is to find a general strategy that they can use to quickly figure out which person will be the last one standing for any number of people.
Why we like this activity
- It’s fun! Students enjoy playing the game and trying to find a strategy to figure out which person will be the last one standing.
- It helps students develop algorithmic reasoning.
- It helps students develop numerical reasoning.
It requires students to engage in mathematical habits of mind:
- Making observations / comparing and contrasting / looking for patterns / making and testing predictions / understanding and explaining when trying to figure out who will be the last one standing.
- It has a low floor and a high ceiling: It's easy for students to start playing the game by trial and error, but finding a strategy to figure out which person will be the last one standing is more challenging!
This activity was developed in collaboration with the Julia Robinson Mathematics Festival.