Discussion
The sequence of folding a piece of paper and the manner in which the folded paper has been cut is shown in the following figures. How would this paper look when unfolded?
- A.
- B.
- C.
- D.
Answer: C
The unfolded paper looks like option 3.
The paper is folded along the diagonal and then again, and a bow-tie shaped hole is cut near the folded point. Unfolding reflects that cut across both fold lines, so four copies appear arranged round the centre of the sheet, each a mirror image of its neighbours. Option 3 shows the four copies turned the way that two reflections produce.
The other options show copies that are turned the wrong way, so they cannot be produced by reflecting the cut across the folds.
To check, imagine opening the second fold first. The cut then appears twice, once on each side of the first fold line, as mirror images. Opening the first fold repeats the pair across the diagonal, giving four copies. The copies in option 3 are mirror images of each other in just that way.
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