Add comprehensive level progression design document covering difficulty scaling and pattern generation
This commit is contained in:
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# Level Progression Design
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## Difficulty Scaling Framework
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## Difficulty Scaling Philosophy
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### Core Progression Principles
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1. **Gradual Complexity Introduction**: Each level adds manageable new challenge
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2. **Pattern Recognition Development**: Allow players to learn through repetition
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3. **Flow State Maintenance**: Balance challenge and skill to prevent frustration
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4. **Confidence Building**: Occasional easier levels to maintain player motivation
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5. **Skill Transfer**: Later levels build on patterns learned earlier
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### Level Structure by Stage
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#### Beginner Levels (1-5)
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**Purpose**: Teach core mechanics and build confidence
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### Core Principles
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1. **Gradual Learning Curve**: Each level introduces complexity at a manageable pace
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2. **Flow State Maintenance**: Difficulty increases to match growing player skill
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3. **Recovery Levels**: Occasional easier levels to prevent frustration
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4. **Skill Validation**: Regular challenges that test mastered concepts
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### Mathematical Progression
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```javascript
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const beginnerLevels = {
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nodeCount: 3-4,
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connectionCount: 2-3,
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timeLimit: 60,
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patterns: [
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'simple_chain', // A→B→C
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'triangle', // A↔B↔C↔A
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'star_simple', // A→B,C,D
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'parallel_lines' // A→B, C→D
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],
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objectives: [
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'Learn click and drag mechanics',
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'Understand dotted line targets',
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'Develop basic pattern recognition',
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'Build confidence with success'
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]
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};
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```
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const levelProgression = {
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// Node count progression
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nodeCount: (level) => Math.min(3 + Math.floor(level / 2), 12),
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#### Intermediate Levels (6-15)
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**Purpose**: Develop pattern recognition and spatial reasoning
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```javascript
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const intermediateLevels = {
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nodeCount: 4-7,
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connectionCount: 3-6,
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timeLimit: 50-55,
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patterns: [
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'hub_networks', // Central node connects to others
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'chain_branches', // Main chain with side branches
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'symmetric_patterns', // Mirror patterns
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'grid_subsets' // Partial grid connections
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],
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objectives: [
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'Recognize hub and spoke patterns',
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'Handle multiple connection points',
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'Develop systematic approach',
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'Improve time management'
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]
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};
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```
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#### Advanced Levels (16-25)
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**Purpose**: Challenge spatial reasoning and strategy
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```javascript
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const advancedLevels = {
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nodeCount: 7-10,
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connectionCount: 6-12,
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timeLimit: 40-50,
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patterns: [
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'complex_webs', // Highly interconnected
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'layered_networks', // Multiple connection layers
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'asymmetric_designs', // Non-obvious patterns
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'efficiency_puzzles' // Optimal path challenges
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],
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objectives: [
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'Handle complex interconnections',
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'Develop strategic thinking',
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'Master time pressure',
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'Recognize advanced patterns'
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]
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};
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```
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#### Expert Levels (26+)
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**Purpose**: Master-level challenges for dedicated players
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```javascript
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const expertLevels = {
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nodeCount: 10-12,
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connectionCount: 8-16,
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timeLimit: 30-45,
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patterns: [
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'maximum_complexity', // Dense interconnections
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'puzzle_variants', // Special rules or constraints
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'artistic_patterns', // Beautiful but complex designs
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'speed_challenges' // Time-focused difficulties
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],
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objectives: [
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'Perfect pattern recognition',
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'Master advanced strategies',
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'Handle maximum complexity',
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'Achieve expert-level flow'
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]
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};
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```
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## Pattern Type Definitions
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### Basic Patterns (Levels 1-5)
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```javascript
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const basicPatterns = {
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linear_chain: {
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description: 'Simple A→B→C→D sequence',
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difficulty: 1,
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nodeRange: [3, 4],
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connectionFormula: 'nodes - 1'
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// Connection complexity
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connectionCount: (level) => {
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const nodes = nodeCount(level);
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return Math.min(nodes - 1 + Math.floor(level / 3), nodes * 1.5);
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},
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simple_triangle: {
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description: 'Three nodes all connected',
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difficulty: 2,
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nodeRange: [3, 3],
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connectionFormula: '3'
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// Time pressure
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timeLimit: (level) => Math.max(30, 60 - Math.floor(level / 3) * 2),
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// Pattern complexity score
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complexityScore: (level) => Math.min(level * 0.8 + 2, 10)
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};
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```
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## Level Archetypes
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### Tutorial Levels (1-3)
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**Purpose**: Teach basic mechanics
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**Node Count**: 3-4
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**Pattern Types**: Simple chains, basic shapes
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**Time Limit**: 60 seconds (generous)
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```javascript
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// Example Level 1 pattern
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const level1 = {
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nodes: 3,
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pattern: [[0, 1], [1, 2]], // Simple chain A→B→C
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type: 'linear_chain',
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tutorial: 'Connect the nodes by dragging from one to another'
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};
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// Example Level 2 pattern
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const level2 = {
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nodes: 4,
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pattern: [[0, 1], [0, 2], [0, 3]], // Hub pattern
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type: 'hub',
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tutorial: 'One node can connect to multiple others'
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};
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```
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### Skill Building Levels (4-10)
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**Purpose**: Develop pattern recognition
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**Node Count**: 4-6
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**Pattern Types**: Hubs, simple networks, parallel chains
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**Time Limit**: 55-60 seconds
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```javascript
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// Level design templates
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const skillBuildingTemplates = {
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doubleHub: {
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description: 'Two hub nodes with overlapping connections',
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complexity: 4,
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example: [[0, 2], [0, 3], [1, 2], [1, 3]]
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},
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basic_star: {
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description: 'One central hub with spokes',
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difficulty: 2,
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nodeRange: [4, 5],
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connectionFormula: 'nodes - 1'
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parallelChains: {
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description: 'Multiple independent connection chains',
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complexity: 3,
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example: [[0, 1], [1, 2], [3, 4], [4, 5]]
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},
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triangle: {
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description: 'Basic geometric shape',
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complexity: 3,
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example: [[0, 1], [1, 2], [2, 0]]
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}
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};
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```
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### Intermediate Patterns (Levels 6-15)
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### Challenge Levels (11-20)
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**Purpose**: Test mastery with complex patterns
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**Node Count**: 6-9
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**Pattern Types**: Complex networks, geometric shapes, asymmetric designs
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**Time Limit**: 45-55 seconds
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```javascript
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const intermediatePatterns = {
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branched_tree: {
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description: 'Tree structure with multiple branches',
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difficulty: 3,
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nodeRange: [5, 7],
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connectionFormula: 'nodes - 1 + Math.floor(nodes/3)'
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const challengeTemplates = {
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star: {
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description: 'Central hub with outer ring connections',
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complexity: 6,
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nodeCount: 7,
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centerNode: true
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},
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partial_mesh: {
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description: 'Partially connected mesh network',
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difficulty: 4,
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nodeRange: [6, 8],
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connectionFormula: 'Math.floor(nodes * 1.5)'
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mesh: {
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description: 'Highly interconnected network',
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complexity: 7,
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connectionDensity: 0.6 // 60% of possible connections
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},
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symmetric_design: {
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description: 'Symmetrical connection patterns',
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difficulty: 4,
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nodeRange: [6, 8],
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connectionFormula: 'varies by symmetry type'
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symmetrical: {
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description: 'Mirror-image patterns',
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complexity: 5,
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symmetryType: 'vertical' // or 'horizontal', 'rotational'
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}
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};
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```
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### Advanced Patterns (Levels 16+)
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### Master Levels (21+)
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**Purpose**: Ultimate skill test
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**Node Count**: 9-12
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**Pattern Types**: Complex geometric shapes, dense networks, multi-hub systems
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**Time Limit**: 30-45 seconds
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## Pattern Generation Algorithm
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### Basic Algorithm
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```javascript
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const advancedPatterns = {
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dense_network: {
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description: 'Highly interconnected nodes',
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difficulty: 5,
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nodeRange: [8, 12],
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connectionFormula: 'Math.floor(nodes * 2)'
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},
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layered_structure: {
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description: 'Multiple connection layers',
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difficulty: 5,
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nodeRange: [9, 12],
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connectionFormula: 'complex algorithm'
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},
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efficiency_puzzle: {
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description: 'Optimal path challenges',
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difficulty: 6,
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nodeRange: [10, 12],
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connectionFormula: 'maximum complexity'
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}
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};
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```
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## Difficulty Adjustment Algorithm
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### Dynamic Difficulty
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```javascript
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function calculateLevelDifficulty(level) {
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const baseNodeCount = 3;
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const nodeGrowthRate = 0.3;
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const maxNodes = 12;
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// Gradually increase node count
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const nodeCount = Math.min(
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Math.floor(baseNodeCount + level * nodeGrowthRate),
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maxNodes
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);
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// Connection count scales with nodes and level
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const connectionMultiplier = 1 + (level * 0.05);
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const baseConnections = nodeCount - 1;
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const connectionCount = Math.floor(baseConnections * connectionMultiplier);
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// Time limit decreases gradually
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const baseTime = 60;
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const timeReduction = Math.floor(level / 3) * 2;
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const timeLimit = Math.max(30, baseTime - timeReduction);
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function generateLevelPattern(levelNumber) {
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const config = getLevelConfig(levelNumber);
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const nodes = generateNodePositions(config.nodeCount);
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const pattern = generateConnectionPattern(nodes, config);
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return {
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nodeCount,
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connectionCount: Math.min(connectionCount, nodeCount * 2),
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timeLimit,
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complexityScore: calculateComplexity(nodeCount, connectionCount)
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nodes,
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targetConnections: pattern,
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timeLimit: config.timeLimit,
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complexity: calculateComplexity(pattern)
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};
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}
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```
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### Complexity Scoring
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```javascript
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function calculateComplexity(nodeCount, connectionCount) {
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const nodeFactor = nodeCount * 0.3;
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const connectionFactor = connectionCount * 0.5;
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const densityFactor = (connectionCount / nodeCount) * 0.2;
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return Math.floor(nodeFactor + connectionFactor + densityFactor);
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function getLevelConfig(level) {
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if (level <= 3) return tutorialConfig(level);
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if (level <= 10) return skillBuildingConfig(level);
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if (level <= 20) return challengeConfig(level);
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return masterConfig(level);
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}
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```
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## Player Progression Metrics
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### Success Indicators
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- **Completion Rate**: >80% for current difficulty tier
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- **Time Efficiency**: Consistent improvement in completion times
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- **Pattern Recognition**: Faster start times (less hesitation)
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- **Error Rate**: Fewer invalid connection attempts
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### Progression Gates
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### Pattern Validation
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```javascript
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const progressionGates = {
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beginnerToIntermediate: {
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criteria: [
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'Complete levels 1-5 with >80% success rate',
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'Average completion time <45 seconds',
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'Less than 2 invalid attempts per level'
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]
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},
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function validatePattern(nodes, connections) {
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const checks = {
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isConnected: validateConnectivity(nodes, connections),
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hasReasonableComplexity: validateComplexity(connections),
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isAesthetic: validateAesthetics(nodes, connections),
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isSolvable: validateSolvability(connections)
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};
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intermediateToAdvanced: {
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criteria: [
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'Complete levels 6-15 with >70% success rate',
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'Handle 6+ node networks confidently',
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'Demonstrate pattern recognition speed'
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]
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},
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return Object.values(checks).every(check => check === true);
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}
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advancedToExpert: {
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criteria: [
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'Complete levels 16-25 with >60% success rate',
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'Master complex interconnected patterns',
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'Maintain performance under time pressure'
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]
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}
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};
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function validateConnectivity(nodes, connections) {
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// Ensure all nodes are part of the pattern (no isolated nodes)
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const connectedNodes = new Set();
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connections.forEach(([a, b]) => {
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connectedNodes.add(a);
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connectedNodes.add(b);
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});
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return connectedNodes.size === nodes.length;
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}
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```
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## Balancing and Tuning
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## Difficulty Balancing
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### Playtesting Feedback Loops
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1. **Immediate Feedback**: Success/failure rates per level
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2. **Completion Analytics**: Time distributions and attempt counts
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3. **Frustration Points**: Levels with high abandonment rates
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4. **Flow Breaks**: Sudden difficulty spikes or boring plateaus
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### Adjustment Parameters
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### Complexity Factors
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```javascript
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const tuningParameters = {
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tooEasy: {
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indicators: ['>95% completion rate', 'Average time <20 seconds'],
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adjustments: ['Add 1-2 connections', 'Reduce time limit by 5s', 'Increase pattern complexity']
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const complexityFactors = {
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nodeCount: {
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weight: 2.0,
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calculate: (nodes) => nodes
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},
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tooHard: {
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indicators: ['<50% completion rate', 'High abandonment rate'],
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adjustments: ['Remove 1-2 connections', 'Add 10s to time limit', 'Simplify pattern type']
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connectionDensity: {
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weight: 1.5,
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calculate: (connections, nodes) => connections.length / (nodes * (nodes - 1) / 2)
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},
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justRight: {
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indicators: ['70-85% completion rate', 'Engaged retry behavior'],
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actions: ['Maintain current parameters', 'Use as template for similar levels']
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patternSymmetry: {
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weight: -0.5, // Symmetric patterns are easier
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calculate: (connections) => calculateSymmetryScore(connections)
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},
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crossingConnections: {
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weight: 1.0,
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calculate: (connections, nodePositions) => countCrossings(connections, nodePositions)
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}
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};
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function calculateLevelComplexity(level) {
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let totalComplexity = 0;
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Object.entries(complexityFactors).forEach(([factor, config]) => {
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const value = config.calculate(level);
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totalComplexity += value * config.weight;
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});
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return totalComplexity;
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}
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```
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### Dynamic Difficulty Adjustment
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```javascript
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class DifficultyAdjuster {
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constructor() {
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this.playerPerformance = [];
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this.adjustmentThreshold = 3; // Adjust after 3 consecutive fails/successes
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}
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recordPerformance(level, completed, timeRemaining) {
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this.playerPerformance.push({
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level,
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completed,
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timeRemaining,
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timestamp: Date.now()
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});
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this.considerAdjustment();
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}
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considerAdjustment() {
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const recent = this.playerPerformance.slice(-this.adjustmentThreshold);
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if (recent.length < this.adjustmentThreshold) return;
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const allFailed = recent.every(p => !p.completed);
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const allSucceeded = recent.every(p => p.completed && p.timeRemaining > 10);
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if (allFailed) {
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this.suggestEasierLevel();
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} else if (allSucceeded) {
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this.suggestHarderLevel();
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}
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}
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suggestEasierLevel() {
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// Reduce complexity by decreasing connections or increasing time
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console.log('Player struggling - suggest reducing complexity');
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}
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suggestHarderLevel() {
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// Increase complexity or reduce time
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console.log('Player excelling - suggest increasing complexity');
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}
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}
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```
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## Level Testing and Validation
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### Playtesting Metrics
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```javascript
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const playtestingMetrics = {
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completionRate: {
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target: '>80% for levels 1-10, >60% for levels 11-20, >40% for levels 21+',
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measure: (attempts, completions) => completions / attempts
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},
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averageTime: {
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target: '50-80% of time limit used',
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measure: (completionTimes, timeLimit) => completionTimes.reduce((a, b) => a + b) / completionTimes.length / timeLimit
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},
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retryRate: {
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target: '<30% of players retry level',
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measure: (retries, attempts) => retries / attempts
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},
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engagementScore: {
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target: 'Players continue to next level >90% of time',
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measure: (continuations, completions) => continuations / completions
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}
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};
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```
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### A/B Testing Framework
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```javascript
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const abTestingLevels = {
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testVariants: [
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{
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name: 'standard_progression',
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description: 'Current difficulty curve'
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},
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{
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name: 'gentler_slope',
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description: 'Slower difficulty increase'
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},
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{
|
||||
name: 'steeper_challenge',
|
||||
description: 'Faster ramp to complexity'
|
||||
class LevelTester {
|
||||
constructor() {
|
||||
this.variants = {};
|
||||
this.results = {};
|
||||
}
|
||||
],
|
||||
|
||||
metrics: [
|
||||
'level_completion_rate',
|
||||
'session_length',
|
||||
'player_return_rate',
|
||||
'user_satisfaction_score'
|
||||
]
|
||||
};
|
||||
addVariant(levelNumber, variantName, pattern) {
|
||||
if (!this.variants[levelNumber]) {
|
||||
this.variants[levelNumber] = {};
|
||||
}
|
||||
this.variants[levelNumber][variantName] = pattern;
|
||||
}
|
||||
|
||||
getVariantForPlayer(levelNumber, playerId) {
|
||||
const variants = Object.keys(this.variants[levelNumber] || {});
|
||||
if (variants.length === 0) return null;
|
||||
|
||||
// Deterministic assignment based on player ID
|
||||
const variantIndex = hashPlayerId(playerId) % variants.length;
|
||||
return variants[variantIndex];
|
||||
}
|
||||
|
||||
recordResult(levelNumber, variantName, result) {
|
||||
const key = `${levelNumber}-${variantName}`;
|
||||
if (!this.results[key]) {
|
||||
this.results[key] = [];
|
||||
}
|
||||
this.results[key].push(result);
|
||||
}
|
||||
|
||||
analyzeResults(levelNumber) {
|
||||
const variants = this.variants[levelNumber];
|
||||
const analysis = {};
|
||||
|
||||
Object.keys(variants).forEach(variant => {
|
||||
const results = this.results[`${levelNumber}-${variant}`] || [];
|
||||
analysis[variant] = {
|
||||
completionRate: results.filter(r => r.completed).length / results.length,
|
||||
averageTime: results.reduce((sum, r) => sum + r.timeUsed, 0) / results.length,
|
||||
playerFeedback: results.map(r => r.satisfaction).filter(Boolean)
|
||||
};
|
||||
});
|
||||
|
||||
return analysis;
|
||||
}
|
||||
}
|
||||
```
|
||||
|
||||
## Recovery and Flow Management
|
||||
## Special Level Types
|
||||
|
||||
### Difficulty Relief Valves
|
||||
- **Confidence Boosters**: Easier levels every 5-7 levels
|
||||
- **Pattern Variety**: Mix familiar and new pattern types
|
||||
- **Time Flexibility**: Slightly longer time limits after difficulty spikes
|
||||
- **Visual Clarity**: Ensure complex levels have clear visual hierarchy
|
||||
### Bonus Levels
|
||||
**Frequency**: Every 10 levels
|
||||
**Purpose**: Reward progress with fun, creative challenges
|
||||
**Characteristics**: Unique mechanics, relaxed time pressure, special visual effects
|
||||
|
||||
### Player Journey Optimization
|
||||
```javascript
|
||||
const playerJourney = {
|
||||
onboarding: {
|
||||
levels: '1-3',
|
||||
focus: 'Mechanics mastery',
|
||||
successRate: '>90%'
|
||||
},
|
||||
### Recovery Levels
|
||||
**Frequency**: After 3 consecutive failures
|
||||
**Purpose**: Rebuild confidence and momentum
|
||||
**Characteristics**: Slightly easier than expected, familiar patterns, generous time
|
||||
|
||||
engagement: {
|
||||
levels: '4-15',
|
||||
focus: 'Skill development',
|
||||
successRate: '70-85%'
|
||||
},
|
||||
### Skill Check Levels
|
||||
**Frequency**: Levels 10, 20, 30, etc.
|
||||
**Purpose**: Validate mastery before advancing to next tier
|
||||
**Characteristics**: Comprehensive challenge using all learned concepts
|
||||
|
||||
mastery: {
|
||||
levels: '16+',
|
||||
focus: 'Expert challenges',
|
||||
successRate: '60-75%'
|
||||
}
|
||||
};
|
||||
```
|
||||
|
||||
This progression system should be continuously refined based on player data and feedback to maintain optimal challenge and engagement throughout the player's journey.
|
||||
This progression system ensures players remain engaged while being appropriately challenged throughout their journey.
|
||||
Reference in New Issue
Block a user