A piece of paper is folded and cut as shown below in the Question figures from…
2024
A piece of paper is folded and cut as shown below in the Question figures from the given answer figures, indicate the pattern that it will appear when it is opened?
Attempted by 44 students.
Show answer & explanation
Rule for paper-folding-and-cutting figures: when a sheet is folded along symmetric fold lines and a notch is then cut through all the folded layers, unfolding reverses each fold and mirrors the cut across every fold line used. So the final pattern repeats the cut once for every layer created by the folds, arranged with mirror symmetry across each fold axis.
The circular sheet is folded once along a vertical diameter, doubling it into two layers (a half-circle).
It is folded a second time along the horizontal radius, doubling it again into four layers (a quarter-circle wedge).
A heart-shaped notch is cut into the folded edge of this quarter wedge, passing through all four layers at once.
Unfolding the second fold reflects the notch across that fold line, giving two mirrored heart-shaped cutouts inside the half-circle.
Unfolding the first fold reflects that pair again across the vertical diameter, giving four heart-shaped cutouts in total — one centred on each of the up, down, left and right directions from the centre, each pointing inward.
Two folds were made, so the unfolded sheet must show 2 × 2 = 4 copies of the cut, symmetric about both the vertical and horizontal axes — never an odd count, never shapes crowded into only one quadrant, and never a cutout profile different from the heart-shaped notch that was actually cut.
Four shapes each shifted off-axis into a corner, with an extra attached loop, breaks the required mirror symmetry about the two fold lines, so it cannot come from this fold sequence.
Four plain triangular notches: the cutout profile itself is not the heart shape that was actually cut, so this is wrong regardless of arrangement.
Four arrow-like V-notches pointing to the centre: again the cutout shape does not match the rounded heart profile cut into the folded wedge.
The pattern that satisfies this — four heart-shaped cutouts, one on each axis direction, all pointing toward the centre, symmetric across both fold lines — is the correct unfolded figure.