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
re: solution is right but logic might be flawed by Charlie)
Charlie wrote: "How did you eliminate 2x3 in the first step? The same perimeter of ten can be achieved by this (with area 6) or 1x4 (with area 4). Both area 6 and area 4 are nonunique (6=3x2=6x1; 4=2x2=4x1)."
1x4 is disallowed from the statement "I am thinking of a rectangle with integer sides, each of which are greater than one inch.".
Therefore 2x3 would correspond to a unique area and perimeter, and both Peter and Paul would have known the other's dimension immediately.

Posted by Penny
on 20050201 07:40:36 