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### Three Holes Puzzle

```Date: 05/02/2002 at 11:59:53
From: Ali
Subject: Three Holes Puzzle

A piece of plywood has three holes it it: a circular hole with a
diameter of 2 cm, a square hole with 2 cm sides, and a triangular hole
with a base and height of 2 cm. What object could both completely plug
each hole AND pass completely through each hole?

Thanks.
-Ali
```

```
Date: 05/03/2002 at 15:43:28
From: Doctor Ian
Subject: Re: Three Holes Puzzle

Hi Ali,

Imagine starting with a board and cutting it so that the cross-section
is 2 cm square: that is, the board would plug the square hole, and you
could slide it all the way through.

2 cm
+----+
2cm   /    /|
+----+ |
|    | |
|    | |
|    | |
|    | |
|    |

Now turn this on its side, and lay it across the triangular hole. Cut
away everything that doesn't fit through the hole, so you end up with
something like this:

plugs the
square hole     plugs the
2 cm           this way        triangular hole
+----+              |           this way
2cm   /    /               |        __
+----+   -            v         /|
\  /    | 2 cm                /
\/     |
-

You have one more direction from which to make it look like a circle.

Can you take it from here?

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

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