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I was wondering if there was a general for formula to calculate the combination of the password lock for the current smart phones

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The following is the condition

  1. We must use four nodes or more to make a pattern at least.
  2. Once anode is visited, then the node can't be visited anymore.
  3. You can start at any node.
  4. A pattern has to be connected.
  5. Cycle is not allowed.

If using 4 as the minimum string for the password with 9 nodes , the result is 389112.

Is there anyway to estimate the number of combinations for 16 nodes, 25 nodes and so on?

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    As @Gerry wrote, they most likely can't. It's most likely just a coincidence.2012-11-26

1 Answers 1

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Since each dot can be the starting point for the pattern, the number of possibilities are as follows:

  1. 4 dots combination (since this is the minimum required): 9 dots (starting points) ^ (raise to the power) 4 = 6,561 patterns
  2. 5 dots combination: 9 dots ^ 5 = 59,049 patterns
  3. 6 dots combination: 9 dots ^ 6 = 531,441 patterns
  4. 7 dots combination: 9 dots ^ 7 = 4,782,969 patterns
  5. 8 dots combination: 9 dots ^ 8 = 43,046,721 patterns
  6. 9 dots combination: 9 dots ^ 9 = 387,420,489 patterns

Total possible number of patterns = 435,847,230 patterns

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    That's not right. The dot sequence must be *connected*.2013-11-10