Calculating valid Pattern Lock combinations for a 3x3 grid…
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Calculating valid Pattern Lock combinations for a 3x3 grid
Hi everyone! I'm looking for a detailed breakdown of the total number of possible combinations for a pattern lock on a standard 3x3 grid. I have two specific scenarios I’d like to compare, and I would love to see the methodology (combinatorics, coordinate-based recursion, or DFS) used to reach the result.
**The Constraints (Standard Android Rules):**
1. **Uniqueness:** Each node can be used only once.
2. **The "Skip" Rule:** You cannot jump over an unused node to reach another node on the same straight line (e.g., connecting (0,0) to (0,2) without hitting (0,1)).
3. **The "Transparent" Exception:** If a node has already been visited, it becomes "passable," and you can jump over it to reach a new node.
**Scenario 1: Standard Android Security**
* What is the total number of valid patterns using **minimum 4 and maximum 9** nodes?
**Scenario 2: Generalized 3x3 Pattern**
* What is the total number of patterns if we lower the minimum to **2 nodes (up to 9)**, while keeping the "no-skip" and "uniqueness" rules active?
**Request:**
If possible, please explain your calculation method. Are you using a brute-force script (DFS), or is there a way to model this through graph theory or coordinate constraints?
Thanks in advance!
#science
Hi everyone! I'm looking for a detailed breakdown of the total number of possible combinations for a pattern lock on a standard 3x3 grid. I have two specific scenarios I’d like to compare, and I would love to see the methodology (combinatorics, coordinate-based recursion, or DFS) used to reach the result.
**The Constraints (Standard Android Rules):**
1. **Uniqueness:** Each node can be used only once.
2. **The "Skip" Rule:** You cannot jump over an unused node to reach another node on the same straight line (e.g., connecting (0,0) to (0,2) without hitting (0,1)).
3. **The "Transparent" Exception:** If a node has already been visited, it becomes "passable," and you can jump over it to reach a new node.
**Scenario 1: Standard Android Security**
* What is the total number of valid patterns using **minimum 4 and maximum 9** nodes?
**Scenario 2: Generalized 3x3 Pattern**
* What is the total number of patterns if we lower the minimum to **2 nodes (up to 9)**, while keeping the "no-skip" and "uniqueness" rules active?
**Request:**
If possible, please explain your calculation method. Are you using a brute-force script (DFS), or is there a way to model this through graph theory or coordinate constraints?
Thanks in advance!
#science
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