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!
When everyone is sitting in a chair, how many ways can just one person sit in the wrong one?
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!
5 responses
The first person in could sit at the wrong chair??
So 8??
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.
When I first read the question I had the same answer as Wam moir. For the desired answer the question seems to be missing a conditional, and could be written as “With everyone seated, how many ways can just one person sit in the wrong chair?
Hi Peter,
Thanks for your comment! I thought I covered that base with a sentence in the first paragraph:
“The meeting starts when there is one person sitting on each chair.”
but maybe I need to tighten the wording further.
I’ve tweaked the question a bit – hopefully there is less confusion from now on.
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