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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: ( You must be logged in to post comments.)
  Subject Author Date
SolutionAnswerMath Man2014-04-02 20:52:39
answerK Sengupta2007-11-12 02:33:09
SolutionJohn Spannenburg2006-03-29 07:12:26
re: And here's my procedure....John Spannenburg2006-03-29 07:09:04
No Subjecttogo172005-12-24 23:41:34
How About This Boys And Girls?Chandra2005-11-19 00:00:28
re: I think I got it hereBrandon2005-05-09 03:54:20
Some ThoughtsI think I got it hereBrandon2005-05-09 03:50:26
re: Any solutions found.nikki2005-05-03 18:01:30
Answer?Stanton2005-05-03 01:26:43
Any solutions found.Stanton2005-05-03 01:23:04
re(2): Correction to Addendum to Another solutionPat Whitaker2005-04-04 18:43:34
re: Addendum to Another solutionPat Whitaker2005-04-04 18:12:15
Another solutionPat Whitaker2005-04-03 05:32:04
My answerDavid2005-04-01 19:08:58
MY SOLN.ravi2005-02-22 11:46:47
my solution and methodjoseph2005-02-21 08:19:21
Solutionpossible spoiler (dont count on it)Angela2005-02-15 11:33:55
re: solutionraye2005-02-10 23:45:58
re(2): solutionCharlie2005-02-07 15:10:53
Questionre: solutionRex2005-02-07 11:09:40
And here's my procedure....sam2005-02-02 07:00:52
I did it by hand and have an excel doc that shows my worksam2005-02-02 06:45:59
re: Possible solution (and the first correct one)Penny2005-02-01 18:28:12
re: Nikki, you were right all along (VB Program solution)nikki2005-02-01 16:37:57
SolutionNikki, you were right all along (VB Program solution)Penny2005-02-01 16:23:24
SolutionsolutionCharlie2005-02-01 16:03:14
re: perplexednikki2005-02-01 15:57:20
QuestionperplexedCharlie2005-02-01 15:42:53
Various comments (spoilers!)nikki2005-02-01 15:37:09
re(3): solution is right but logic might be flawedPenny2005-02-01 08:17:29
re(2): solution is right but logic might be flawedPenny2005-02-01 07:40:36
re: solution is right but logic might be flawedCharlie2005-02-01 05:21:46
Solutionsolution is right but logic might be flawedJim Ratajczak2005-02-01 05:05:54
SolutionDid anyone have this solution yet?Charlie2005-02-01 03:04:32
Milind is right, not bonkers (spoilers!)nikki2005-01-31 15:43:22
SolutionMy solutionPenny2005-01-31 13:28:00
Possible solutionMilind2005-01-31 10:02:18
re: Answer + SolutionMilind2005-01-31 09:14:31
Another answerMike2005-01-31 07:29:47
re: Answer + SolutionPenny2005-01-29 14:48:20
re: Answer?nikki2005-01-28 20:46:17
Answer?casey2005-01-28 20:31:34
SolutionAnswer + Solutionnikki2005-01-28 20:29:26
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