I think I've solved it For the first node, you have 7 choices. For the second, you have 6 and for the last, you have 5. So the initial answer is 5*6*7 = 210 However, because of that central node interfering with everything, you have to subtract a number of possibilities The possibilities where you use any node and immediately its diametrically opposite one. There are twelve such possible ways those pairs of nodes and (assuming you're allowed to use the central one then the top left and bottom right) 4 nodes for each such possibility. 4*12=48 So if we take-away that from the initial we get 210-48 = 162 possibilities.
I think I've solved it
ReplyDeleteFor the first node, you have 7 choices. For the second, you have 6 and for the last, you have 5. So the initial answer is 5*6*7 = 210
However, because of that central node interfering with everything, you have to subtract a number of possibilities The possibilities where you use any node and immediately its diametrically opposite one. There are twelve such possible ways those pairs of nodes and (assuming you're allowed to use the central one then the top left and bottom right) 4 nodes for each such possibility. 4*12=48
So if we take-away that from the initial we get 210-48 = 162 possibilities.