Solution
The solution has X and Y as 4 and 13 (or vice versa), with P initially knowing the product is 52 and S knowing the sum is 17.
Initially P does not know the solution, since
- 52 = 4 × 13 = 2 × 26
and S knows that P does not know the solution since all the possible sums to 17 within the constraints produce similarly ambiguous products. However, each can work out the solution by eliminating other possibilities following the other's statements and that is enough for the reader to find the solution given the constraints.
Read more about this topic: Impossible Puzzle
Famous quotes containing the word solution:
“There’s one solution that ends all life’s problems.”
—Chinese proverb.
“I can’t quite define my aversion to asking questions of strangers. From snatches of family battles which I have heard drifting up from railway stations and street corners, I gather that there are a great many men who share my dislike for it, as well as an equal number of women who ... believe it to be the solution to most of this world’s problems.”
—Robert Benchley (1889–1945)
“Give a scientist a problem and he will probably provide a solution; historians and sociologists, by contrast, can offer only opinions. Ask a dozen chemists the composition of an organic compound such as methane, and within a short time all twelve will have come up with the same solution of CH4. Ask, however, a dozen economists or sociologists to provide policies to reduce unemployment or the level of crime and twelve widely differing opinions are likely to be offered.”
—Derek Gjertsen, British scientist, author. Science and Philosophy: Past and Present, ch. 3, Penguin (1989)