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.

ABJ11 Oct 10, 2019

#1**0 **

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

ElectricPavlov Oct 10, 2019

#3**0 **

...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