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Topic: Re: Happy New Year - Response to solution
Replies: 2   Last Post: Jan 16, 1998 10:17 AM

 Messages: [ Previous | Next ]
 kaplan.5@osu.edu Posts: 205 Registered: 12/4/04
a "quarter" solution and a new puzzler
Posted: Jan 16, 1998 10:17 AM

G. A. Page wrote:
>
> Jim,
>
> Aren't you the clever one...Nice problem! I'm going to use this exercise
> as an example of the importance of obtaining a better visual image via
> making a sketch of the particulars.
>
> Here's a similar problem that I hope you and everyone else finds
> interesting.
>
> 4 Quarter Problem
>
> Take 4 U.S. quarters and arrange them to form a square. Like this:
>
> OO
> OO Place each quarter together as close as possible . In other
> words, the sides of the quarters are tangent to the quarter above or
> below or left or right of said quarter.. This should still leave some
> space in the middle that resembles a diamond. This space eventually
> tapers off and ends where the quarter meet. (I couldn't provide a
> picture of this, sorry)
>
> The centers of the quarters are the vertices of a square. If the
> what is the area of the shaded region?
>
> Good luck!

This is a cute problem we give to our future elementary school
teachers...BUT...Are we to assume that "the shaded region" is the
diamond-shaped area between quarters?

In the square formed, there are four quarter circles which are
equivalent in area to 1 circle.

The diamond-shaped area = area of the square - area of 1 circle.

This statement can be written with mathematical symbols using
radius = Q, that is: (2Q)^2 - Â¼Q^2 = 4Q^2 - Â¼Q^2 = (4-Â¼)Q^2

HERE IS A PROBLEM SOMEONE SENT ME. IT WAS POSED ON THE NATIONAL

Simplify the polynomial: (x+a)(x-b)(x+c)(x-d)...(x-z). There are 26
factors altogether. (The answer may surprise you.)

Rose Kaplan
Math Lab
OSU Newark, Ohio

Date Subject Author
1/12/98 JamesF119@aol.com
1/16/98 mathlab@juno.com
1/16/98 kaplan.5@osu.edu