Inspired by Parth Sankhe

Probability Level 5

Again, it's examination day, but now there are 7 students S 1 , 2 , … , 7 S_{1,2,\ldots,7} in a class.

They are supposed to sit in a circle, but no student S i S_i is allowed to sit next to either of S i − 1 S_{i-1} or S i + 1 S_{i+1} . S 1 S_1 and S 7 S_7 also aren't allowed to sit next to each other.

How many different seating arrangements are possible?

Details and Assumptions:

  • Two arrangements that are rotations or mirror images of each other are considered different .

Inspired by this problem by Parth Sankhe


The answer is 322.

Henry U by Henry U , 17, Germany

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1 solution

Tolga Gürol
Dec 13, 2018

Is it possible to solve this without coding?

0 Helpful 0 Interesting 0 Brilliant 0 Confused

I did it by hand because I don't know enough about coding. Of course, I didn't count all 322 arrangements, but rather 322 7 = 46 \frac {322}{7} = 46 since there are 7 different rotations for each one.

Henry U - 2 years, 6 months ago

I tried to find a formula for n students. Is there any formula?

Alapan Das - 2 years, 2 months ago

1 pending report

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