android lock password combinations

passwords combinations combinatorics
rplusg picture rplusg · Aug 8, 2011 · Viewed 31k times · Source

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)

Answer

Dante May Code picture Dante May Code · Aug 8, 2011

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.

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