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?

first of all as peter says he has' no idea' so it implies that it is not a square where the sides are primes and that the area is more than 6.
paul's comment shows that if u write the perim. as sum of 2 nos then there cant be a case where both nos are prime. so we are left a set of 7 nos. which can be the possible perim.
petrs comment tells that there are still more than two possibilities.
whe n u break these nos into sum of 2 nos. then if u find the area there is only 1 no. 11 that has only one solution so it is 11 which is the sum of the 2 sides and it matches with 17 so the 2 sides are 56

Posted by ravi on 2005-02-22 11:46:47