You understand that you you don't need to go from one circle to an adjacent one. For example if we put A,B,C on the X-axis and 1,2,3 on the Y-axis, your pattern can go from A1 to C2? Plus I think that there's just a minimum of 4 circle touches required - not sure what the maximum number is. So I don't know the math but that makes for a heck of a lot of combinations.