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Guess My Number

How it works

In this game, one player picks a number between 1 and 100, and the other player tries to figure out what it is by asking only yes / no questions.

What is the minimum number of questions you need to ask in order to guarantee that you figure out the other person’s number? What if their number is between 1 and 200? 1 and 1000? What if you lose if you get three “no” answers?

Why we like this activity:

  • It’s fun! The game is suspenseful and entertaining.

  • It helps to develop algorithmic reasoning.

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

    • Finding and using strategies to figure out the other person's number with as few questions as possible.

    • Making and testing predictions about the maximum number of questions you might have to ask using a given strategy.

    • Finding similarities and differences between playing the game when the number is in different ranges.

    • Finding and using strategies to try to avoid losing when playing the game where you lose after the third "no".

    • Finding and using strategies to figure out the other person's number with as few questions as possible while also avoiding losing when playing the game where you lose after the third "no".

  • It has a low floor and a high ceiling: It's easy for students to get started playing the game, but finding a good strategy is challenging, especially for the version of the game where you lose after the third “no”.