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Possible Duplicate:
Combination of smartphones' pattern password

I have the following problem:

9dots_numbered

As you can see, this is a 9 dot pattern. I'm looking to find the number of all possible combinations according to several rules. Here are the rules of the problem:

  1. Only straight lines can be used to connect the dots.
  2. At least 4 dots must be connected.
  3. If you connect 2 dots directly, when there's a dot in between, it will also be crossed (so if you try to connect 1->3, you'll actually connect 1->2->3). This rules exist if rule #6 is not in effect.
  4. Diagonal lines are allowed (you can connect from 2->6, even from 4->9).
  5. You must use one continuous line to connect all dots (The continuous line can be broken into straight lines only).
  6. Once a dot is connected, it may not be connected again.

Examples for valid connections:

1->2->3->6 1->(5)->9->(8)->7 1->6->7->4->2->3->9->8->5 //Note that when passing from 3 to 9, 6 is not selected again. 

Invalid:

1->2->3 1->2->3->2 4->(5)->6->5 

I honestly don't know how to even begin to approach this. And would appreciate any help :)

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    @Madara: Whether a question is a duplicate doesn't depend on whether the original question has been answered. Note that both questions have been answered in the meantime, and the answer to this duplicate question needlessly duplicates the answer to the original question.2012-11-26
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    The picture and accepted answer don't seem to indicate that diagonal connections are allowed. As it stands, the problems are close, but not duplicates.2012-11-26
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    @joriki: Wrong, this question does not duplicate the answer given in the suggested duplicate. It's different.2012-11-26
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    @robjohn: I don't think that the fact that the OP chose to clarify the original question in an obscure comment under an incorrect answer instead of editing it should keep the question from being interpreted as intended, especially not if the OP explicitly states that the accepted answer is incorrect because the question was misunderstood and that the present question was intentionally asked to duplicate the intended question, and a correct answer to the intended question has been given under the original question in the meantime.2012-11-26
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    @robjohn: I belabour this point because questions being intentionally duplicated out of a misunderstanding that they're not duplicates as long as the original hasn't been satisfactorily answered is a recurring problem, and in my view following Madara's argument in this case would contribute to that problem by validating an argument based on an answer deemed unsatisfactory.2012-11-26
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    I did not view the video mentioned on the other post until now. It does state that diagonals are allowed. Therefore, this is a duplicate and I will close and merge.2012-11-26

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