Question

A paper is folded in a given pattern and it is cut at the end. Identify which pattern is formed when the paper is unfold.

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

The three folds are along both diagonals and a mid-line, so the unfolded pattern is symmetric about both diagonals and both mid-lines: each hole is repeated 8 times.

Answer 1

The Correct Option is D

The first fold is along one diagonal, the second along the other diagonal and the third along a mid-line of the square, so the final triangle is one eighth of the square and the unfolded pattern is symmetric about both diagonals and both mid-lines.
The final triangle has three holes: one close to the centre side, one near the right angle on the edge, and one near the corner. Reflecting each hole in all eight symmetries gives: eight holes in a ring around the centre; a pair of holes on each side of the square close to the middle of the side; and a pair of holes at each corner.
Only option (4) has all of these. Options (1), (2) and (3) have single holes at the middle of some sides and are not symmetric about the mid-lines.
Answer: (4) the last pattern