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        riddles >> medium >> SQUARE DIVISION
        
(Message started by: pa0pa0 on Jul 28^th, 2002, 3:45am)

Title: SQUARE DIVISION
Post by pa0pa0 on Jul 28^th, 2002, 3:45am

>draw a square. divide it into four identical squares. remove
>the bottom left hand square. now divide the resulting shape
>into four identical shapes.

There's a lovely riddle which starts with the solution to this one;

first show someone how to divide the L-shaped area into four identical shapes, and then say

"Now, for the follow-on, take a whole square (instead of
three-quarters of a square), and divide it into five instead
of four) identical shapes."

Title: Re: SQUARE DIVISION
Post by Your Name Here on Jul 30^th, 2002, 11:58am

To state the riddle in another way - Take an L-shape made up of 3 joined squares, and divide it into 4 identical shapes.

To figure this out, I tried dividing each of the 3 squares into 4 smaller squares. This meant the L shape was made of 12 smaller squares. Then I tried finding a 3-smaller-square shape that could fill up the space. The shape is an L shape, with one of the smaller L's nestled in the inside corner of the larger L.

Here it is, with o's, x's, a's and c's representing the four identical shapes filling the L:
------
-ooxx-
-oaax-
---ac-
---cc-
------

Title: Re: SQUARE DIVISION
Post by me on Aug 2^nd, 2002, 6:55am

Ummm.. Pa0pa0... is this just supposed to make people try to think hard about something simple?

For a square with sides of length X, just draw 4 lines horizontally at a spacing of X/5.

Or am I missing something?

Title: Re: SQUARE DIVISION
Post by pa0pa0 on Aug 3^rd, 2002, 11:55am

on 08/02/02 at 06:55:21, me wrote:

Ummm.. Pa0pa0... is this just supposed to make people try to think hard about something simple?

Yes. Many times I've had people, who solve part 1 in just a few minutes, stumped for a very long time on part 2. If one eventually has to tell them the answer, it's advisable to stand a safe distance away.