Promising them an increase in their allowance if they get the answer, I offer my two sons, Peter and Paul, the following puzzler:

"I am thinking of a rectangle with integer sides, each of which are greater than one inch. The total perimeter of the rectangle is no greater than eighty inches."

I then whisper the total area to Peter and the total perimeter to Paul. Neither of them are allowed to tell the other what they heard: their job is to work out the rectangle's dimensions.

Their subsequent conversation goes like this:

Peter: Hmmm... I have no idea what the perimeter is.
Paul: I knew you were going to say that. However, I don't know what the area is.
Peter: Still no clue as to the perimeter...
Paul: But now I know what the area is!
Peter: And I know what the perimeter is!

What are the dimensions of the rectangle?

(In reply to Nikki, you were right all along (VB Program solution) by Penny)

"[Sorry, I wasn't being sarcastic. You were right all along in the sense that you picked up right away on Paul's  subtle first statement, although your first answer was not correct. Remember my comment: "I may be stumbling over that subtle hint 'I knew you were going to say that' by Paul" ? At least I was right about that.] "

=)  I saw your title, and before reading the comment I was already composing a reply to you... something along the lines of  "No I wasn't... I had the right logic all along, but made an error at first so I wasn't RIGHT all along."

At least you can say your 4x4 answer was right for a different problem =D

Posted by nikki on 2005-02-01 16:37:57