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
Answer + Solution by nikki)
Some thoughts on Nikki's solution. (Possibly, I have misunderstood the solution or missed something :) )
Possible sides for rectangle with area 52: 2 * 26, 4 * 13
Once Paul says he does not know the area, we have only possible perimeters as: 22, 34, 46, 54, 58, 70, and 74
Now, when Peter says for the second time that he does not know the perimeter, he is wrong; in the sense that the only possible perimeter can be 34 from sides 4, 13 (We can rule out 2,26 because 2,26 gives perimeter as 56  which is not present in the above list).
So, may be 4, 13 is not the answer....

Posted by Milind
on 20050131 09:14:31 