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The Android unlock pattern

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The Android unlock pattern

The Android unlock pattern has 9 dots on the screen organized in a 3×3 matrix. To unlock the phone a so called pattern has to be drawn on the screen, which means connecting certain points in a certain order. So how many valid patterns are there? For this let’s first observe the rules of pattern drawing:

at minimum 4 dots have to be used
at maximum 9 dots can be used
one dot can be used only once
the order in which the dots are connected matters (thus making it a directed graph)
dots are connected with a straight line meaning that all points on the path of the line get connected
The last rule introduces some conditional connection paths. When connecting two points with a straight line it is valid only if there is no unused point in the way. For example: you cannot connect points 1 and 3 unless point 2 is already is used. So by default drawing a line from 1 to 3 will result in the pattern 1→2→3. However if point 2 is used the transition 1→3 becomes valid, such as in 2→1→3, making a previously invalid transition valid (1→3).

Also what some people seem to omit is that connecting points in a slight diagonal is possible (especially on Android 4, since the dots became smaller) such as 2→7.

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i'd say its

4P9+ 5P9 +6P9 +7P9 +8P9 +9P9 = 9!/5! +9!/4! +9!/3! +9!/2! +9!/1! +9!/0! = 3024 +15120 +60480 +181440 +362880 +362880 = 985824

Edited by phil1882
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i'd say its

A good start.

Someone has create a program to list all the possibility and there are only 1/3 possibilities of your answer.

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