GATE2025_CS1_Q9

A square paper, shown in figure (I), is folded along the dotted lines as shown in the figures (II) and (III). Then a few cuts are made as shown in figure (IV). Which one of the following patterns will be obtained when the paper is unfolded?
Note: The figures shown are representative.

✅ Final Answer:

The correct pattern is (A).

🔹 Short Answer:

The paper is folded twice, creating four layers. All cuts are made through these four layers. When unfolding, the cuts are mirrored. The square cut at the corner (which is the paper's center) unfolds into a diamond. The triangular cut at the edge unfolds into four symmetrical triangular holes. Option (A) is the only one showing this correct pattern.

🔸 Long Answer:

To solve this puzzle, we reverse the folding process, mirroring the cuts at each step.

Step 1: Analyze the Folds and Cuts

The paper is folded into four layers. The final folded piece (Fig. IV) has two cuts: a small square at the top corner and a small triangle at the bottom edge.

Step 2: The Unfolding Process

We work backwards from Figure IV to Figure I.

• First Unfold (from IV to II): The piece is unfolded horizontally. The square cut at the corner of the fold line is mirrored, creating a diamond shape on the new fold's centerline. The triangular cut on the outer edge is also mirrored, creating a second triangular cut.
• Second Unfold (from II to I): The resulting larger triangle is unfolded along the main diagonal. The diamond at the center is now fully formed. The two triangular cuts are mirrored across this diagonal, creating two more for a total of four outer holes.

Step 3: Evaluate the Final Pattern

The final, fully unfolded paper will have:

1. A single diamond-shaped hole in the center.
2. Four triangular holes, one in each quadrant, pointing towards the corners.

This configuration perfectly matches the pattern shown in Option (A).

Bibliography:
- Indu, S. (2018). A New Approach to Reasoning. Arihant Publications. (Chapter on Paper Folding & Cutting).

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