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Rectangular Logic (Posted on 2005-01-28) Difficulty: 4 of 5
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?

No Solution Yet Submitted by Sam    
Rating: 3.7500 (12 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution is right but logic might be flawed | Comment 12 of 44 |
(In reply to solution is right but logic might be flawed by Jim Ratajczak)

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 non-unique (6=3x2=6x1; 4=2x2=4x1).
  Posted by Charlie on 2005-02-01 05:21:46

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