When the paper is folded in a given pattern and is cut at the end. Identify which pattern is formed when the paper is unfold?
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Count the folds: three folds give 8 layers, so every hole in the folded piece gives 8 holes, and the unfolded sheet must be mirror-symmetric about both diagonals and both mid-lines.
The square is folded three times: first along a diagonal, then along the line joining the centre to the right-angle corner, and then along the symmetry line of the resulting triangle. The final piece is a small right triangle that is 1/8 of the square and has 8 layers of paper. Four holes are punched in this small triangle: one near the corner at the centre of the sheet, one near the middle of the slanted edge (the diagonal), one near the outer corner of the sheet and one near the middle of the outer side. Every hole is repeated in all 8 layers, so the opened sheet has 4 x 8 = 32 holes, and the pattern is a mirror image about both diagonals and both mid-lines of the square. This gives: a ring of 8 holes around the centre (a pair on each side of every mid-line), 8 holes in pairs along the four half-diagonals, 8 holes in pairs at the four corners (one on each side of each diagonal) and 8 holes in pairs at the middle of the four sides. Option (1) has only about 22 holes and option (3) only about 24, so they cannot be right. Option (2) has pairs of holes high up near the vertical mid-line and a centre ring that is not mirror-symmetric, so it does not match. Option (4) has the full set of 32 holes: 8 around the centre, 8 in the diagonal pairs, 8 corner holes and 8 side-middle holes, all mirror-symmetric. Answer: (4) the fourth pattern (32 holes, symmetric about both diagonals and both mid-lines)
