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N=sum of primes between smallest and largest prime factor of N (inclusive).

Find all possible values for the composite number N below 300.

(No Solution Yet, 2 Comments) Submitted on 2018-10-19 by Ady TZIDON   
Difficulty: 4 of 5 Bonus: Rectangular Logic (in Logic) Rating: 3.75
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, 44 Comments) Submitted on 2005-01-28 by Sam   
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