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.

  • 1
    $\begingroup$ @Len - In terms of what is considered "identical", the 4 rotational equivalents of a given pattern is all that really matters given the requirement that "my" patterns are already symmetrical reflectively. (i.e. it doesn't matter if "S is the same as mirrored-S", since it's impossible for that to be the correct answer anyway) $\endgroup$
    – Alconja
    Feb 11, 2015 at 2:26
  • $\begingroup$ That being said, it's plausible (likely?) that a given "line" is producible via multiple different non-rotationally equivalent patterns. And ultimately, it's the line of the pattern that's important for this puzzle, so any of those given answers would be considered "correct". $\endgroup$
    – Alconja
    Feb 11, 2015 at 2:30

2 Answers 2


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


  • $\begingroup$ The one you have as the previous pattern fails the reflective symmetry (as per rule 3 & thus 2). $\endgroup$
    – Alconja
    Feb 11, 2015 at 3:50
  • $\begingroup$ The symmetry is about the resulting line, so your "previous" one still fails. If you don't have an android phone, draw it on paper and you'll see that there's no mirroring. Whereas the one you have listed as your "current" pattern is mirrored down the 258 line. $\endgroup$
    – Alconja
    Feb 11, 2015 at 5:05
  • 1
    $\begingroup$ nice star you found there! +1 $\endgroup$
    – Novarg
    Feb 11, 2015 at 10:28
  • 1
    $\begingroup$ Well done. Interestingly, I wasn't aware of your solution and my "current" one is actually different again. But it certainly satisfies the rules, so I'm still accepting the answer. :) $\endgroup$
    – Alconja
    Feb 11, 2015 at 10:30
  • 1
    $\begingroup$ Another awesome pattern, but still not my intended answer. :D ...if you're interested, I've created a spin off puzzle with an additional rule. $\endgroup$
    – Alconja
    Feb 11, 2015 at 23:46

So your previous pattern looked like an alphanumeric character, used all 9 dots and was symmetrical. Alphanumeric characters: ABCDEFGHIJKLMNOPQRSTUVWXYZ1234567890. Out of these there are some asymmetric: FGJLNPQRSZ245679. That leaves us with: ABCDEHIKMOTUVWXY138.
Now let's throw out the ones that can't fit using all 9 dots: ACDHIKOTUVXY1. This leaves us with: BEMW38. Because you will always have an "opening" in your pattern, we can throw out B and 8, so only possible answers are: EMW3. But E, M and W and 3 are actually same pattern, just turned 90 degrees, so your old pattern looked like E, so most probably that Impossible 3-Ends: 854693217

So now we should find your current pattern:

Because we only know that it is symmetric and uses all 9 dots we can assume the following pattern to be your current one: gonna find it out soon and update my answer

  • $\begingroup$ Really nice work of pinning down the characters, although you lost the 0 in the first step, but it is symmetrical and should only be eliminated in the second step not using all 9 dots. $\endgroup$
    – Falco
    Feb 12, 2015 at 13:06
  • 1
    $\begingroup$ Why are L and Q not considered reflective across the diagonal? Both would be taken out because they can't be drawn on the pad, but they should still be valid for step 1. $\endgroup$
    – DonielF
    Jul 3, 2017 at 4:54

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