On a phone screen with 9 dots arranged in a 3x3 matrix such that there must be a minimum on 4 dots connected, each dot can only be connected once, and intermediary dots between two other dots must be connected, how many different patterns can be made? Essentially how many phone unlock patterns are there?

I have only been able to find solutions with brute forcing, using scripts, etc. Is there a way to mathematically find the number of patterns?

Guest Jan 3, 2019