Pool Party Puzzle answer (4/07) (fwd)

Judy Ann Brown (judyann@dimacs.rutgers.edu)
Mon, 7 Apr 1997 21:55:22 -0400


I would like some comments on this week's POW...
Here is the text:

Mr. and Mrs. Gomez just put a pool in their back yard. Mr.
Gomez is a mathematics professor at the local college and
Mrs. Gomez is a computer design engineer. For luck, they
insisted that all the dimensions of their rectangular pool be
square numbers. The area the pool covers must be a square
number, the length and width must be square numbers and
the difference between the length and width must also be a
square numbers. Their back yard is a rectangle that is 20 feet
by 30 feet, and they purchased the largest 'square dimension'
pool that would fit in their yard. What are the dimensions of
their pool?

Now here is the clever answer sent in by a 12th grade student...

------------ Forwarded Message begins here ------------
From: stof@bigfoot.com
Date: Sun, 6 Apr 1997 22:36:54 -0400 (EDT)
To: judyann@dimacs.rutgers.edu
Subject: Pool Party Puzzle answer (4/07)

From: Chris Hanusa
School: Taylor Allderdice High School
Grade: 12
Answer: I see at least two answers to this problem.
the square numbers less than 30 are 1,4,9,16,25.
Because 16 and 25 work as dimensions, (25=5^2, 16=4^2, 25-16=3^2)
we could stop at a 16x25 ft^2 pool.

But I KNOW that Mr. and Mrs. Gomez want the largest pool possible.
Thus, they realize that they could change the pool dimensions into
centimeters, giving a maximum of 609 cm x 914 cm.
Mr. and Mrs. Gomez realize that they can make a pool that is:
576 cm x 900 cm, as 576=24^2, 900=30^2, 900-576=324=18^2.
this is much larger than before, and they are both happy.


------------ Forwarded Message ends here ------------

Now what do you think would happen if we chose a smaller unit of measure, say
millimeters? Would we get a larger pool? What about inches?
And what is smaller than a millimeter?

What about a proof?

Any comments are welcome.


visit the PCTM web site at: http://home.ptd.net/~pctm/main.html
visit the Puzzle of the Week (POW) page at:
Judy Ann Brown
Pleasant Valley Middle School
Brodheadsville, Pa 18322