All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 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: ( Back to comment list | You must be logged in to post comments.)
 re: And here's my procedure.... | Comment 41 of 44 |
(In reply to And here's my procedure.... by sam)

I believe your solution is correct however I don't have your spreadsheet so could not really check the logic totally of course.  I have done a spreadsheet which also uses a process of elimination and also deduce one unique solution as being 5 x 6.  Not sure why the problem is still marked as not having a solution yet unless the author? found fault with your logic in the spreadsheet?  Maybe he could confirm that...
 Posted by John Spannenburg on 2006-03-29 07:09:04

 Search: Search body:
Forums (0)