Thursday, April 19, 2018

geometry - Help! I've forgotten my phone's lock pattern!


I have an Android phone with a pattern lock screen, which if you've never seen one allows you to unlock your phone using a pattern drawn on the screen over a 3x3 grid of dots.


So for example, if we number the dots as follows:


1 2 3
4 5 6

7 8 9

then valid lock patterns may be created by drawing lines connecting 1 > 2 > 3 > 4, or 1 > 5 > 9 > 8 > 7.


Note, there are a few rules restricting what constitutes a valid unlock pattern:



  • Any given dot can only be used once (however you can cross back over a previously used dot, if you can connect to another unused dot on the other side)

    • Eg. 1 > 2 > 3 is valid, 2 > 1 > 2 is invalid, but 2 > 1 > 3 is valid (goes back over the 2, but doesn't re-include it in the actual code)




  • If your line crosses directly over a previously unused dot, it is automatically included in the code

    • Eg. Attempting to create a code of 1 > 3 > 4 would automatically become 1 > 2 > 3 > 4




What I remember about my specific lock pattern:



  1. It used all 9 dots

  2. The line representing the pattern has reflective symmetry


  3. It is different to my previous pattern which also followed rules 1 & 2

  4. My previous pattern looked like an alphanumeric character


What is current my lock pattern? What was my previous lock pattern?


For the purposes of this puzzle, we'll ignore the fact that there will be multiple "correct" answers achieved by simply rotating by multiples of 90 degrees. In other words a pattern of 1 > 2 > 3 will be considered identical to 3 > 6 > 9.


Edit: Given that Len found two valid solutions below, and neither was my intended solution, I've added an extension puzzle with an additional rule.



Answer



Added 4th solution.


I think your previous pattern was:




M which is also called impossible 3 ends shown below - 854693217

3 ends



And you current pattern is one of:



- a type of star left below - 857342619
- or a geometric pattern center below - 851962473
- or a modified M right below - 254693817

LockPatterns



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