QB_PH_GA_027: Analytical & Spatial Aptitude

A square sheet of paper is folded in half once from left to right, and then folded in half again from top to bottom. A single circular hole is punched straight through all layers of the folded paper. When the sheet is unfolded completely, how many circular holes will appear on the sheet?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Fold Layer Multiplicity**: - Initial unfolded state: $1$ layer. - After 1st fold (left to right): $2$ layers. - After 2nd fold (top to bottom): $2 \times 2 = 4$ layers. 2. **Punching Action**: A single through-hole punches through all 4 co-located layers in the quarter-square. 3. **Unfolding**: Because the two folds correspond to reflection across two orthogonal lines of symmetry, the hole replicates into 4 distinct quadrants. 4. **Official Integer Answer**: 4.