perplexus.info :: Logic : Rectangular Logic

Rectangular Logic (Posted on 2005-01-28)

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
Puzzle Answer	K Sengupta	2024-01-19 23:07:30
hi	saim malik	2023-01-19 02:42:25
tour travel company in india	imran malik	2023-01-16 00:31:55
references	Steven Lord	2022-10-08 19:48:45
Pilgrimage Tourism	Kashmir Tours	2022-10-08 02:01:32
No Subject	Kashmir Tours	2022-10-08 02:00:05
Puzzle Thoughts	K Sengupta	2022-09-19 05:31:56
No Subject	Whia1967	2022-09-19 04:56:43
Answer	Math Man	2014-04-02 20:52:39
answer	K Sengupta	2007-11-12 02:33:09
Solution	John Spannenburg	2006-03-29 07:12:26
re: And here's my procedure....	John Spannenburg	2006-03-29 07:09:04
No Subject	togo17	2005-12-24 23:41:34
How About This Boys And Girls?	Chandra	2005-11-19 00:00:28
re: I think I got it here	Brandon	2005-05-09 03:54:20
I think I got it here	Brandon	2005-05-09 03:50:26
re: Any solutions found.	nikki	2005-05-03 18:01:30
Answer?	Stanton	2005-05-03 01:26:43
Any solutions found.	Stanton	2005-05-03 01:23:04
re(2): Correction to Addendum to Another solution	Pat Whitaker	2005-04-04 18:43:34
re: Addendum to Another solution	Pat Whitaker	2005-04-04 18:12:15
Another solution	Pat Whitaker	2005-04-03 05:32:04
My answer	David	2005-04-01 19:08:58
MY SOLN.	ravi	2005-02-22 11:46:47
my solution and method	joseph	2005-02-21 08:19:21
possible spoiler (dont count on it)	Angela	2005-02-15 11:33:55
re: solution	raye	2005-02-10 23:45:58
re(2): solution	Charlie	2005-02-07 15:10:53
re: solution	Rex	2005-02-07 11:09:40
And here's my procedure....	sam	2005-02-02 07:00:52
I did it by hand and have an excel doc that shows my work	sam	2005-02-02 06:45:59
re: Possible solution (and the first correct one)	Penny	2005-02-01 18:28:12
re: Nikki, you were right all along (VB Program solution)	nikki	2005-02-01 16:37:57
Nikki, you were right all along (VB Program solution)	Penny	2005-02-01 16:23:24
solution	Charlie	2005-02-01 16:03:14
re: perplexed	nikki	2005-02-01 15:57:20
perplexed	Charlie	2005-02-01 15:42:53
Various comments (spoilers!)	nikki	2005-02-01 15:37:09
re(3): solution is right but logic might be flawed	Penny	2005-02-01 08:17:29
re(2): solution is right but logic might be flawed	Penny	2005-02-01 07:40:36
re: solution is right but logic might be flawed	Charlie	2005-02-01 05:21:46
solution is right but logic might be flawed	Jim Ratajczak	2005-02-01 05:05:54
Did anyone have this solution yet?	Charlie	2005-02-01 03:04:32
Milind is right, not bonkers (spoilers!)	nikki	2005-01-31 15:43:22
My solution	Penny	2005-01-31 13:28:00
Possible solution	Milind	2005-01-31 10:02:18
re: Answer + Solution	Milind	2005-01-31 09:14:31
Another answer	Mike	2005-01-31 07:29:47
re: Answer + Solution	Penny	2005-01-29 14:48:20
re: Answer?	nikki	2005-01-28 20:46:17
Answer?	casey	2005-01-28 20:31:34
Answer + Solution	nikki	2005-01-28 20:29:26

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