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03 May 2005

PizzaQ Besbol Question still unanswered

A reminder ... there is still no Certified Solution to the Vleeptron PizzaQ Besbol Problem. Amy submitted a solution

(1080/sqrt(2))^2 + ((1080/sqrt(2)) - ((1080 x sqrt(2)) - 726 inches))^2

= answer^2

which we are having a bit of ambiguity with, and we have asked her to re-submit her solution using { [ ( ) ] } instead of ( ( ( ) ) ). Until she does, and we can evaluate her solution, Vleeptron considers the Problem still Unsolved.

(Sometimes we look at her solution and it seems to require us to take the square root of a negative number, which is Evil.)

Here is the problem (described so non-Besbolistas can understand it):

A regulation Besbol Diamond is a diamond (square) 90 feet on each side. The bottom corner is Home Plate. The other corners are

1st Base (right corner)
2nd Base (top), and
3rd Base (left corner)

On a line between Home Plate and 2nd Base, the Pitcher is 60 feet 6 inches from Home. (1 foot = 12 inches)

What is the distance between the Pitcher and 1st Base?

The answer must use only Whole Numbers, and any arrangement of addition, subtraction, multiplication, division, and square root.

We have previously established that this is a Pythagorean Right-Triangle Thing. You know:

x² + y² = z²


Blogger Amy said...

The knuckles crack again...and for the last time.

After several sheets of hotel stationary, I think I have it! I checked and rechecked the math, even though I'll admit that I was confused for a while there.

Error number one was that when Mike was explaining where the pitcher's mound was, I mistakenly believed it was closer to 2nd base than to home. That was a duh-Amy moment. It is closer to home than to 2nd.

Having said that...the answer in as reduced-but-still-in-whole-numbers-form:

The square root of:

{47041-[21780(sqrt 2)]}

(hope that came out)

How I got it?

Side A (the one going from first to the exact center of the field) is (90 sqrt(2))/2.

Side B (the little bit between exact center of the field to the pitcher's mound) is (90 sqrt(2))/2) - (121/2)

Square A...square B...add 'em together and take the square root of that (with a little reducing). Since the square of A is a nice whole number (4050) and part of the square of B has a whole number (the square of B is (30841 - 21780 sqrt(2))/4 ).

I hesitate to ask whether I've got it this time :)


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