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In case someone don't know what a pattern lock is, they are like this:

example of a pattern lock

I am curious on the probability of randomly cracking one of these 'passwords', given that the length of the grid is 3x3 and that we know the pattern length (e.g number of lines).

Also, you may or not noticed but the pattern can go in both + and x directions.

Note: we can have multiple lines that go to a single dot, but we can never draw a line above another line (I think some apps allow this, but for this question lets assume we will not).

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    Perhaps a duplicate of [Combination of smartphones' pattern password.](http://math.stackexchange.com/q/37167/242)2012-12-06

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The answer arrived at the end in sunflower's link, 389112 is actually incorrect. It doesn't take into account patterns connect via 2 steps along a line, or a peg jump if the middle point is already used. The correct answer thus becomes 766752. Here's the explanation given by Yoyo Zhou, a Google engineer, along with his algorithm :-

http://www.quora.com/How-many-combinations-does-Android-9-point-unlock-have

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    So can '1-8-2' be done without doing '1-8-5-2'? (My phone can't do this.) And the result 389112 of course concerns those moves. ('1-2-3', '2-1-3', '2-3-1' are valid and different, but '1-3-2' can't be done.)2014-05-22