How would you cut a hole in a sheet 20 cm by 30 cm so that you could crawl through the hole without ripping the paper?

Answer 1

Let the four corners be ABCD (which are the longer and shorter sides doesn't matter). Then:

1. Fold the sheet in half putting A onto D and B onto C; let the two ends of the fold be X and Y to give a rectangle XYBA.
2. Slice along the fold (XY) most of its length BUT ensure that it is NOT sliced at a short distance from each end.
3. Make cuts from the sliced fold (XY) towards the other edge (AB) through both sides of the folded paper, cutting the fold (XY) BUT stopping a short distance from the other edge (AB)
4. Make cuts between these cuts towards the fold (XY) from the other edge (AB) through both sides of the folded paper, cutting side AB but stopping short of XY.
5. The piece of paper can now be opened out into a large ring which you should be able to step through.

The shorter the distance between the cuts the larger the ring will be.

In the following diagram, XY is the folded edge, cut along the plusses (+) - the dots (inside the rectangle) show the bits of paper that form the ring.

.........................................................................................

.X.--++++++++++++++++++++++++++++++--.Y.

.....|.+......+.......+.......+......+......+.......+.......+......+..|....

.....|.+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..|....

.....|.+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..|....

.....|.+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..|....

.....|.+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..|....

.....|.+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..+..|....

.....|.....+.......+.......+......+......+.......+.......+......+......|....

.A.----+-----+-----+----+----+-----+----+----+----.B.

.D.................................................................................C.

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