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
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