Blog

Difficulty: Fun


Eight people come together for a very important meeting. There are eight chairs around the table, and each one has a little sign with a name so everyone knows where they should sit. The meeting starts when there is one person sitting on each chair. But sometimes, people end up in the wrong places!


There’s only one way for everyone to sit in the right seat, but there are 28 ways that two people could end up in the wrong seat. And three people in the wrong place could happen in 112 different ways!

How many ways can just one person sit in the wrong chair?

Need a hint?

Just try it! Draw a table with chairs, and some people, and see what happens when you start matching them up

Brainteaser answer

It’s impossible for only one person to sit in the wrong seat. If seven people are sitting in the right seats, there’s only one space left for the last person – and it’s their seat!

2 responses

  1. Wam moir Avatar
    Wam moir

    The first person in could sit at the wrong chair??
    So 8??

    1. David Shaw Avatar
      David Shaw

      Hi Wam,
      It’s a good thought, but there’s a bit more to think about.

      If the first person sits in someone else’s seat, that second person doesn’t have anywhere to sit any more! Wherever they go, they too will be in the wrong seat.

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

By submitting this form, you give CSIRO permission to publish your comments on our websites. Please make sure the comments are your own. For more information please see our terms and conditions.

Why choose the Double Helix magazine for your students?

Perfect for ages 8 – 14

Developed by experienced editors

Engaging and motivating

*84% of readers are more interested in science

Engaging students voice