I have chosen two different numbers greater than N but less than M. I tell their sum to Mr. S and their product to Ms. P. The following conversation ensues:

Mr. S: I cannot determine the two numbers.
Ms. P: I cannot determine the two numbers either.
Mr. S: I still cannot determine the two numbers.
Ms. P: Now I can determine the two numbers.
Mr. S: Now I can determine the two numbers also.

Find the greatest value of M for which this puzzle has a unique solution, for N=1, N=2 and N=3.

(In reply to re: Clarification needed (Question) by Larry)

That isn't how I interpret this. M and N are not the numbers to be guesses and for which one person knows the sum and the other knows the product. It states that each of the two numbers (say x and y) is greater than N and less than M. In order to make x and y guessable, both guessers must know the bounds, N and M, in which x and y are to be found.

Posted by Charlie on 2024-01-08 13:43:04