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        riddles >> medium >> Rectangle
        
(Message started by: harpoo4n5 on Aug 10^th, 2007, 11:33am)

Title: Rectangle
Post by harpoo4n5 on Aug 10^th, 2007, 11:33am

A farmer tells his sons that he will give them the ranch if they can guess the dimensions of the ranch. He tells son A the area and son B the perimeter. He tells both that the perimeter is lesss than 80, and no side exceeds 2, in whole units. The sons cannot tell each other the area or the perimeter.

A: I don't know the dimesions of the ranch.
B: I knew you were going to say that
A: I STILL don't know the dimensions
B: well....I know the dimensions now.
A: I know the dimensions now, too.

what are the dimensions?

Title: Re: Rectangle
Post by ThudanBlunder on Aug 10^th, 2007, 12:06pm

Don't you mean that no side exceeds 20 and that all measurements are in whole units?

Title: Re: Rectangle
Post by harpoo4n5 on Aug 10^th, 2007, 12:13pm

There was a rancher who had two sons. One day he was considering giving his ranch to his boys. He took his first son, D, aside and told him in strictest confidence the AREA of the ranch. He then took his second son, J, aside and told him in
strictest confidence the PERIMETER of the ranch. He also told both boys together that the ranch was a perfect rectangle, that the PERIMETER of the ranch did not exceed 80 miles and that each side of
the ranch was not less than two miles in length, and that all measurements were in whole miles. He then promised them that if they could tell him the DIMENSIONS of the ranch without revealing to each other what he had told them in confidence, in that case he would give them the ranch.

The conversation between the two boys went as follows:

D said, "I don't know what the dimensions of the ranch are."

J responded, "I knew you were going to say that D!"

Then D said, "Well, I STILL don't know what the dimensions are!"

So J said, "Well, I know what the dimensions are now!"

And D concluded the conversation by saying, "Then I know what the dimensions are too!"

There was no other conversation between the boys. They went to their father, told him the dimensions of the ranch, and their father kept his word and gave them the ranch.

WHAT ARE THE DIMENSIONS OF THE RANCH?

The closest i could come to was that since its a perfect rectangle, then one side it 1.6 times the other (golden ratio) and so
1.6x^2 = AREA
2(x + 1.6x) = PERIMETER

Title: Re: Rectangle
Post by ThudanBlunder on Aug 10^th, 2007, 12:16pm

This (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1100930971) might help.

Title: Re: Rectangle
Post by harpoo4n5 on Aug 10^th, 2007, 4:20pm

I'm not sure how though.
The information that is available is:

xy = AREA
2(x+y) = PERIMETER
PERIMETER <= 80
x > 2; y > 2
And from the perfect rectangle:
x = 1.62y

Given the above information, I'm still not sure how to slove the problem. What might help was assuming that the PERIMETER is 80 and then writing out the combinations and selecting the one which satisfies the condition: x = 1.62y (15,25) but taking the PERIMETER to be 80 is probably an incorrect assumption to begin with.

Title: Re: Rectangle
Post by ThudanBlunder on Aug 10^th, 2007, 4:59pm

The crux of the problem (which is not easy) is in the conversation between A and B.

However, there seems to be an issue with the problem statement.
As the golden ratio is an irrational number, X and Y cannot both be whole numbers, or even fractions.

Title: Re: Rectangle
Post by mikedagr8 on Aug 11^th, 2007, 6:19am

Yes, for this problem to work, the numbers must be integers. Wow, that problem was massive. It was nice reading it, i wouldn't be able to solve it, but was enjoyable to read.