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How many ways are there to put 9 differently colored beads on a $3\times3$ grid if the purple bead and the green bead cannot be adjacent (either horizontally, vertically, or diagonally), and rotations and reflections of the grid are considered the same?

 Oct 15, 2020
 #1
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There are 408 ways to place the beads.

 
 Oct 17, 2020
 #2
avatar+111131 
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I doubt this is correct.

 

Scenarios

1 2 3
4 5 6
7 8 9

 

1 Purple in 1 and green in 3

2 Purple in 1 and green in 6

3 Purple in 1 and green in 9

4 Green in 1 and purple in 6

5 Purple in 2 and green in 7

6 Purple in 2 and green in 8

Maybe that is it

 

7!*6 = 30240

 
 Oct 18, 2020

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