Question 1
A paper undergoes three folds: horizontally, then vertically, then diagonally. A single hole is punched at the center of the final triangular shape. What is the complete unfolded pattern?
Advanced Competition-Level Solution (Triple Fold):
Step 1 - Triple Fold Complexity:
- Sequence: horizontally, then vertically, then diagonally
- Layer progression: 1 → 2 → 4 → 8 layers
- Final shape: Complex triangular stack
- Symmetry axes: horizontal, vertical, and diagonal
Step 2 - Mathematical Foundation:
- Three folds = 2³ = 8 layers
- Each fold adds a symmetry axis
- Combined symmetries create complex pattern
- Hole count: 1 punch × 8 layers = 8 holes
Step 3 - Final Pattern:
- Eight holes total
- Complex symmetrical arrangement
- Not a simple grid pattern
- Result: Eight holes in complex symmetric pattern
Competition Insight: Triple folds with mixed directions create patterns that defy simple row/column descriptions.