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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? 

Please help me with this problem.

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 
Associated Topics:
High School Higher-Dimensional Geometry
High School Puzzles
Middle School Higher-Dimensional Geometry
Middle School Puzzles

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