Question 1
Detect the nested (hierarchical) rule system:
Figure 1:
Figure 2:
Figure 3:
Figure 4:
What comes next?
HIERARCHICAL RULE DETECTION:
LEVEL 1 ANALYSIS - Outer Shape Pattern:
Step 1: Identify shapes by counting sides
- Figure 1: Triangle (3 sides)
- Figure 2: Square (4 sides)
- Figure 3: Pentagon (5 sides)
- Figure 4: Hexagon (6 sides)
Rule 1 (Outer): Shape gains +1 side per step
LEVEL 2 ANALYSIS - Inner Element Pattern:
Step 2: Count dots inside each shape
- Figure 1: 1 dot
- Figure 2: 2 dots
- Figure 3: 3 dots
- Figure 4: 4 dots
Rule 2 (Inner): Number of dots increases by +1 per step
NESTED RULE HYPOTHESIS:
TWO independent hierarchical rules:
1. Outer rule: Polygon sides = 3, 4, 5, 6, ...
2. Inner rule: Dot count = 1, 2, 3, 4, ...
CORRELATION CHECK:
Both patterns follow same arithmetic progression (n+1)
Correlation: dot count = shape sides - 2 ✓
VERIFICATION:
- Figure 1: 3 sides, 1 dot (3-2=1) ✓
- Figure 2: 4 sides, 2 dots (4-2=2) ✓
- Figure 3: 5 sides, 3 dots (5-2=3) ✓
- Figure 4: 6 sides, 4 dots (6-2=4) ✓
APPLICATION:
Figure 5 should have:
- Outer: 6 + 1 = 7 sides (heptagon)
- Inner: 4 + 1 = 5 dots
- Verification: 7 - 2 = 5 ✓
ADVANCED NESTED RULE TECHNIQUES:
- Analyze each level independently
- Check for correlations between levels
- Verify consistency across all levels
- Apply all rules to predict next state
- Cross-verify using relationships
COMMON MISTAKES TO AVOID:
- Analyzing only one level
- Missing the relationship between levels
- Not verifying correlation formulas
- Applying only one rule to prediction
- Incomplete hierarchical decomposition
LEVEL 1 ANALYSIS - Outer Shape Pattern:
Step 1: Identify shapes by counting sides
- Figure 1: Triangle (3 sides)
- Figure 2: Square (4 sides)
- Figure 3: Pentagon (5 sides)
- Figure 4: Hexagon (6 sides)
Rule 1 (Outer): Shape gains +1 side per step
LEVEL 2 ANALYSIS - Inner Element Pattern:
Step 2: Count dots inside each shape
- Figure 1: 1 dot
- Figure 2: 2 dots
- Figure 3: 3 dots
- Figure 4: 4 dots
Rule 2 (Inner): Number of dots increases by +1 per step
NESTED RULE HYPOTHESIS:
TWO independent hierarchical rules:
1. Outer rule: Polygon sides = 3, 4, 5, 6, ...
2. Inner rule: Dot count = 1, 2, 3, 4, ...
CORRELATION CHECK:
Both patterns follow same arithmetic progression (n+1)
Correlation: dot count = shape sides - 2 ✓
VERIFICATION:
- Figure 1: 3 sides, 1 dot (3-2=1) ✓
- Figure 2: 4 sides, 2 dots (4-2=2) ✓
- Figure 3: 5 sides, 3 dots (5-2=3) ✓
- Figure 4: 6 sides, 4 dots (6-2=4) ✓
APPLICATION:
Figure 5 should have:
- Outer: 6 + 1 = 7 sides (heptagon)
- Inner: 4 + 1 = 5 dots
- Verification: 7 - 2 = 5 ✓
ADVANCED NESTED RULE TECHNIQUES:
- Analyze each level independently
- Check for correlations between levels
- Verify consistency across all levels
- Apply all rules to predict next state
- Cross-verify using relationships
COMMON MISTAKES TO AVOID:
- Analyzing only one level
- Missing the relationship between levels
- Not verifying correlation formulas
- Applying only one rule to prediction
- Incomplete hierarchical decomposition