What are all the possible pattern locks?
Pattern locks have become increasingly popular in the modern era of smartphones and other devices. These locks provide a unique and visually appealing way to secure your device, offering a balance between security and ease of use. In this article, we will explore the different types of pattern locks and the total number of possible combinations they can offer.
The most common type of pattern lock is the circular pattern lock, which is widely used on Android devices. This lock requires the user to draw a pattern on a circular grid, connecting at least four dots. The complexity of the pattern can vary, with users able to connect as many dots as they wish.
To calculate the total number of possible combinations for a circular pattern lock, we need to consider the number of dots and the number of ways they can be connected. For a circular grid with n dots, the number of possible combinations can be calculated using the formula (n-1)! / 2.
For example, a 3×3 grid has 9 dots, so the number of possible combinations would be (9-1)! / 2 = 8! / 2 = 20,160. However, this formula assumes that all patterns are unique, which is not the case. Many patterns are symmetrical, meaning they can be mirrored or rotated to create different patterns. To account for this, we need to divide the total number of combinations by the number of symmetrical patterns.
For a 3×3 grid, there are 4 symmetrical patterns (up, down, left, right). Therefore, the actual number of unique combinations for a 3×3 circular pattern lock is 20,160 / 4 = 5,040.
As the size of the grid increases, the number of possible combinations grows exponentially. For instance, a 5×5 grid has 25 dots, resulting in 9,378,160 possible combinations. When considering symmetrical patterns, the number of unique combinations is reduced to 9,378,160 / 8 = 1,171,720.
Another type of pattern lock is the linear pattern lock, which is often used on iOS devices. This lock requires the user to draw a straight line across a grid, connecting at least four dots. The complexity of the pattern can vary, with users able to connect as many dots as they wish.
Calculating the total number of possible combinations for a linear pattern lock is simpler than for a circular pattern lock. For a grid with n dots, the number of possible combinations is simply n-1, as the user only needs to connect n-1 dots to create a pattern.
For example, a 3×3 grid has 9 dots, so the number of possible combinations would be 9-1 = 8. However, this formula does not account for symmetrical patterns, which can be eliminated by dividing the total number of combinations by the number of symmetrical patterns.
For a 3×3 grid, there are 2 symmetrical patterns (up and down). Therefore, the actual number of unique combinations for a 3×3 linear pattern lock is 8 / 2 = 4.
In conclusion, the total number of possible pattern locks varies depending on the type of lock and the size of the grid. While circular pattern locks offer a wide range of combinations, linear pattern locks provide a more limited but still secure option. By understanding the different types of pattern locks and their potential combinations, users can choose the best security solution for their needs.
