Android's Locking Pattern
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Join For Freefor the rest of this discussion, i will use the following convention to designate a locking pattern:
0  1  2 
3  4  5 
6  7  8 
 it needs to contain at least four dots (and obviously, no more than nine).
 once a dot is lit, it can't be used again.

you can use one or several "knight moves", such as in [0 5 4 2]:
in this example, the knight move is between 0 and 5.  you cannot go over an unlit dot without lighting it. for example, the pattern [0 2 1 4] is illegal, because moving your finger between 0 and 2 will light 1.

once a dot is lit, you can use it to reach another unlit dot. for example, both [0 4 3 5] and [0 4 5 3] are legal:
this example is a bit ambiguous but you get the idea: i trace [0 4 5] and then i slide over 4 again to reach 3.
with these constraints in place, i wondered how many combinations were actually possible, so i wrote a short program to simulate it. it turns out there are quite a few: 389,112. here is a breakdown:
4 dots: 1624 solutions
5 dots: 7152 solutions
6 dots: 26016 solutions
7 dots: 72912 solutions
8 dots: 140704 solutions
9 dots: 140704 solutions
total: 389112
if you're not convinced, here is a full list of all the four dot patterns (the page uses a big canvas object, it might take a few seconds to load).
still, i'm not sure my calculations are right, so i'd like you, dear reader, to confirm my numbers, and optionally explain how you coded your solution...
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