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 Any solutions found. by Stanton)

Hi Colin, and welcome to Perplexus!

Actually, the fact that it says "No Solution Yet" in the problem has nothing to do with the comments we post.  "No Solution Yet" refers to the OFFICIAL solution that the author wants to post.

The fact that the official solution is not up yet only means the author hasn't put it up yet, and doesn't mean the comments are right or wrong.

You might want to visit the FAQ page.  There's a link to it between the Search box and the Chatter box.

Enjoy!

Posted by nikki on 2005-05-03 18:01:30