Discussion
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.
- A.
- B.
- C.
- D.
Answer: A
The unfolded pattern is (A).
The first fold is along the diagonal from the top-left to the bottom-right corner, and the second folds the remaining triangle along the line from its right-angle corner to the centre, leaving the top quarter of the square with four layers. Unfolding repeats each cut in all four triangular quarters, reflected across the two diagonals.
The triangular cut at the middle of the top edge, pointing outwards, therefore appears at the middle of all four edges, each pointing outwards: up at the top, down at the bottom, left and right at the sides. The notch on the left edge of (IV) lies on the first fold line, so it opens into a square hole, and that square appears in two opposite corners, top-left and bottom-right. The slot near the right edge lies beside the second fold line and opens into a pair of bars, forming the hook shapes at the top-right and bottom-left.
Option (B) shows diamonds instead of squares, option (C) has the top and bottom triangles pointing inwards, and option (D) has a single square at the centre, so only (A) matches.
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