Punching Game The fold is a line of symmetry. Punch holes at different locations of a folded square sheet of paper using a punching machine and create different symmetric patterns.

Question

Homi · Accepted Answer

Understand the Question

Folding a paper in half forms a crease that acts as the line of symmetry (mirror line).
Punching a hole through the folded layers penetrates multiple layers at the same relative position.
When unfolded, each punch produces symmetric pairs of holes positioned at equal distances on opposite sides of the fold line.

Step 1 · Fold the Paper

Take a square sheet of paper and fold it in half. The crease formed represents the line of symmetry. Diagram 1

Step 2 · Punch a Hole

Punch a hole through the folded paper using a hole punch. The punch goes through both overlapping layers. Diagram 2

Step 3 · Unfold to Reveal the Symmetric Pattern

Unfold the sheet of paper. Two holes are visible, each positioned as a mirror image of the other across the central fold line. Diagram 3

Answer

The fold line serves as the line of symmetry, resulting in a symmetric pattern where holes are equidistant and mirrored across the crease.

Common Mistakes

Punching on the Fold Line: Punching directly on the crease produces only one centered hole instead of two symmetric holes.
Number of Holes: Forgetting that punching through $n$ folded layers produces $n$ distinct holes upon unfolding.

Question 3

More questions in FIO