Lots of people use the pattern unlock feature on Android phones. Don’t know why this liking for Pattern over Pin or Password. But I guess that it has to do with the fact that pattern unlock is unique to Android’s vs Windows Phones or iPhones.
Anyways, ever wondered how many combinations are possible on these 9 points arranged 3 x 3? We had an interesting conversation over evening tea one day and I sat to do some math.
First, the conditions for pattern lock.
- The pattern should connect at least four dots.
- The dots in the pattern must be distinct.
- If the line segment connecting any two consecutive dots in the pattern passes through any other dots, the other dots must have previously been in the pattern.
- Not many know of this rule. People usually don’t cross over an already connected point.
- The other thing which most of the people don’t know is the possibility to go thru the gap and join a point which is not immediately adjacent..
The number of combinations possible with 4 to 9 dots are…
- 4 dots, 1,624 combinations
- 5 dots, 7,152 combinations
- 6 dots, 26,016 combinations
- 7 dots, 72,912 combinations
- 8 dots, 140,704 combinations
- 9 dots, 140,704 combinations
So the total number of possible combinations are 389,112.
Now, the second question is, if you brute force to unlock a pattern, what is the maximum time taken? Consider the phone doesn’t lock itself out permanently but locks for 30 seconds after 5 tries. Incidentally, you are allowed 5 tries before the lock screen is suspended for 30 seconds (both PIN and pattern). In pattern, the limit for tries is 20 before it locks out completely and asks for the Google account and password.