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avatar+18 

Find the number of ways of arranging the numbers 1, 2, 3, ...  9 in a circle, so that the sum of any three adjacent numbers is divisible by 3. (Two arrangements are considered the same if one arrangement can be rotated to obtain the other.

 Oct 10, 2019
edited by ABJ11  Oct 10, 2019
edited by ABJ11  Oct 10, 2019
edited by ABJ11  Oct 12, 2019
edited by ABJ11  Oct 12, 2019
 #1
avatar+19324 
+4

Just put them in a circle in order   1 -2 -3-4-5-6-7-8-9     voila!  (well....that is ONE way)

 

 

and here is another   1-3-5-7-9-2-4-6-8

 
 Oct 10, 2019
edited by ElectricPavlov  Oct 10, 2019
edited by ElectricPavlov  Oct 10, 2019
 #2
avatar+19324 
+3

Here is a third one    4-8-6-7-2-9-1-5-3

 
ElectricPavlov  Oct 10, 2019
 #3
avatar+19324 
+3

...and you can shift all of these.....take the first three numbers and put them in the middle

 

456 123 789

 

792 135 468

 

729 486 153         Well, I have found 6 so far     I do not know how to calculate the number possible though !!

 
ElectricPavlov  Oct 10, 2019
 #4
avatar+18 
+1

Ok thanks

 
 Oct 10, 2019

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