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### Cutting Slits in a Piece of Paper

```
Date: 02/01/2002 at 10:01:23
From: Scottie Plyler
Subject: Hole in paper

How can you cut a hole in a piece of paper so a person can go through
it?
```

```
Date: 02/01/2002 at 12:09:37
From: Doctor Ian
Subject: Re: Hole in paper

Hi Scottie,

Take a piece of paper.  Fold it in half:

+---------------------+  <--- edge of fold
|                     |
|                     |
|                     |
|                     |
+---------------------+

Near the left and right sides, and in the middle, cut a slit from the
folded edge almost, but not quite, to the other edge:

+--.-------.-------.--+  <--- edge of fold
|  .       .       .  |
|  .       .       .  |
|  .       .       .  |
|  .       .       .  |
|                     |
+---------------------+

Now cut two slits in between these slits, coming from the other
direction. Again, don't go all the way to the fold:

+--.-------.-------.--+  <--- edge of fold
|  .       .       .  |
|  .   .   .    .  .  |
|  .   .   .    .  .  |
|  .   .   .    .  .  |
|      .        .     |
+------.--------.-----+

Now cut across the fold, except at the very ends:

+--.................--+  <--- edge of fold
|  .       .       .  |
|  .   .   .    .  .  |
|  .   .   .    .  .  |
|  .   .   .    .  .  |
|      .        .     |
+------.--------.-----+

Before making this last cut, if you unfold the paper, it should look
like this:

+------.--------.-----+
|      .        .     |
|  .   .   .    .  .  |
|  .   .   .    .  .  |
|  .   .   .    .  .  |
|  .       .       .  |
|  .       .       .  | <------ edge of fold
|  .       .       .  |
|  .   .   .    .  .  |
|  .   .   .    .  .  |
|      .        .     |
|      .        .     |
+------.--------.-----+

So the last cut goes here:

+------.--------.-----+
|      .        .     |
|  .   .   .    .  .  |
|  .   .   .    .  .  |
|  .   .   .    .  .  |
|  .       .       .  |
|  .................  | <------ edge of fold
|  .       .       .  |
|  .   .   .    .  .  |
|  .   .   .    .  .  |
|      .        .     |
|      .        .     |
+------.--------.-----+

(It's just easier to make the cut while the paper is still folded.)

Now, if you grab the two points labeled A and B,

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

and gently pull them apart, you should find that you've made a
surprisingly large hole in the paper! By making more slits, you can
make the hole even bigger:

+-.---.---.---.---.-+ <--- edge of fold
| .   .   .   .   . |
| . . . . . . . . . |
| . . . . . . . . . |
| . . . . . . . . . |
| . . . . . . . . . |
|   .   .   .   .   |
+---.---.---.---.---+

Cut enough slits, and you could drive a _car_ through the hole.

or anything else.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Geometry
Elementary Puzzles
Elementary Two-Dimensional Geometry
Middle School Geometry
Middle School Puzzles
Middle School Two-Dimensional Geometry

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