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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.

(I) a square; (II) folded along the diagonal from top-left to bottom-right; (III) the triangle folded again from its right-angle corner to the middle of the long side; (IV) the result, point down, with a triangle cut at the top centre and small cuts on the two slanting edges

  • A.Unfolded square with a filled square at the top left, a stepped notch at the top right, an L-shaped notch at the bottom left
  • B.Unfolded square with a diamond at the top left and bottom right, a stepped notch at the top right, an L-shaped notch at the bottom left and triangles at the side midpoints
  • C.Unfolded square with a filled square at the top left and bottom right, a stepped notch at the top right, an L-shaped notch at the bottom left and triangles at the side midpoints
  • D.Unfolded square with a stepped notch at the top right, a filled square at the centre, an L-shaped notch at the bottom left and triangles at the side midpoints

Answer: A

The unfolded pattern is (A).

Follow the folds. The first fold is along the diagonal from top-left to bottom-right; the second folds that triangle along the line from its right-angle corner to the middle of its long side. In figure (IV), the top edge is made of all four original sides of the square laid on top of each other, the left slanting edge is the first fold, and the right slanting edge is the second fold.

  • The triangle cut at the middle of the top edge lies on all four original sides, so it unfolds to a notch at the midpoint of each side, every one pointing out of the square. This rules out (C), whose top and bottom notches point inward.
  • The cut on the left slanting edge is a right-angled triangle whose long side lies on the first fold. Opening a fold doubles a shape across the fold line, and a right triangle doubled across its 45° hypotenuse becomes an upright square. So there are upright squares near the top-left corner and, from the second fold, near the bottom-right corner. This rules out (B), which shows tilted squares, and (D), which has a single square in the centre.
  • The small cut touching the right slanting edge (the second fold) opens into an L-shaped cut near the top-right corner, and the first fold repeats it near the bottom-left corner, as all four options show.

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