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 perplexed by Charlie)

Charlie: you have some duplicates (like 5x6 and 6x5 or 11x12 and 12x11).  When you start, you should only have 361 rectangles.

So your final list is correct, just notice that 22 is actually a unique perimeter since the "two" rectangles are the same.

Hope this helps!

Posted by nikki on 2005-02-01 15:57:20