Countdown

How it works

Countdown is a 2-player game. Here's how to play:

  • Players take turns removing counters (or chips).
  • On each turn, a player can remove either 1 or 2 counters.
  • The player who removes the last counter (so there are no counters left) wins.

Can you beat an expert at this game if you're allowed to choose how many counters to start with and whether to go 1st or 2nd? Can you beat an expert no matter how many counters you start with if you're allowed to choose whether to go 1st or 2nd?

In this activity, students start by playing the game against each other. When they're familiar with the game and have started to develop some intuition and basic strategies, they switch to playing against an expert. Their goal is ultimately to be able to beat an expert with any number of counters, as long as they get to decide whether they go first or second.

After students find a strategy that allows them to do this, they explore variations of the game with different rules (for example, where you can take 1, 2, or 3 instead of just 1 or 2, or where the player who removes the last counter loses instead of winning), seeing if they can beat an expert at these games as well.

Why we like this activity

  • It’s fun! Students enjoy playing the game and figuring out how to beat an expert.
  • It helps to develop algorithmic and game-theoretic reasoning.

  • It requires students to engage in mathematical habits of mind:

    • Finding and using strategies to beat an expert with specific numbers of counters.
    • Making and testing predictions about whether you'll be able to beat an expert with a specific number of counters.
    • Finding and using strategies to beat an expert at Rook’s Move with any number of counters.
    • Understanding and explaining your strategy to beat an expert with any number of counters.
  • It has a low floor and a high ceiling: Students can start playing the game by trial and error, but figuring out how to beat an expert is more challenging!
 
 

This activity was developed in collaboration with the Julia Robinson Mathematics Festival.