+1768 Find the number of ways of choosing three circles below, so that no two circles are next to each other.
0 We can do this by casework:
Case 1: CORNERS
Each corner has \(5\) circles we can choose that are not next to it (The 5 on the border). There are 4 corners so, \(4\times5=20\)
Case 2: EDGES
Each edge has 3 circles we can choose that are not next to it (The 3 opposite to it). There are 4 edges so, \(4\times3=12\)
so: \(20+12=\boxed{32}\)
Note: there woudve been a third case with the center but the center is next to all the cricles in a 3x3 grid
ggwp :)
