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passwordscombinationscombinatorics

android lock password combinations

I just came across with this interesting question from my colleague. I'm trying now, but meanwhile I thought I could share it here.

With the password grid shown in the Android home screen, how many valid passwords are possible? min password length: 4 max: 9 (correct me if I'm wrong)

Solution

  • Summary

    The full combinations of 4 to 9 distinctive numbers, minus the combinations which include invalid "jump"s.

    The Long Version

    The rule for Android 3x3 password grid:

    • one point for once

    • cannot "jump" over a point

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    The author of the original post used Mathematica to generate all 985824 combinations.

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    Because there is no "jump", several pairs of consecutive points are invalid.

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    Delete all invalid combinations to reach the result.

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    The combinations for 4-to-9-point paths are respectively 1624, 7152, 26016, 72912, 140704, 140704.

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    The Original Post In Chinese

    The reference is from guokr, a site alike Stack Exchange Skeptics in the form of blogs.