Impossible Puzzle

The Impossible Puzzle, also named Sum and Product Puzzle is a puzzle called "impossible" because it seems to lack sufficient information for a solution. It was first published in 1969 (Hans Freudenthal, Nieuw Archief Voor Wiskunde, Series 3, Volume 17, 1969, page 152). The name "Impossible Puzzle" was coined by Martin Gardner (Scientific American Volume 241, December 1979). The puzzle is solvable, though not easily. There exist many similar versions of puzzles.

Puzzle

"Given are X and Y, two integers, greater than 1, are not equal, and their sum is less than 100. S and P are two mathematicians; S is given the sum X+Y, and P is given the product X*Y of these numbers."

* "P says "I cannot find these numbers."
* "S says "I was sure that you could not find them."
* "P says "Then, I found these numbers."
* "S says "If you could find them, then I also found them."

"What are these numbers?"

Solution

The solution is: "X"=4, "Y"=13

See also

* List of impossible puzzles

External links

* [http://people.scs.fsu.edu/~burkardt/fun/puzzles/impossible_puzzle.html Puzzles] by John Burkardt
* [http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/logic_sum_product The Impossible Problem] by Torsten Sillke
* [http://mathforum.org/library/drmath/view/55655.html Two Mathematicians Problem] on mathforum
* [http://www.cs.otago.ac.nz/staffpriv/hans/sumpro/sumproAusAI.pdf Model Checking Sum and Product]