Two perfect logicians, S and P, are told that integers x and y have been chosen such that x and y are both greater than 1 and x and y sum to something less than 100. S is given the value x+y and P is given the value xy. They then have the following conversation.
Given that the above statements are true, what are the two numbers?P: I cannot determine the two numbers.
S: I knew that.
P: Now I can determine them.
S: So can I.
Posts
As BAP figured out the solution (by elimination) is S = 17 = 4 + 13 and P = 52 = 4*13.
ReplyDeleteOther solutions (x,y,S,P) are (16,111,127,1776),
(201,556,757,111756), and (421,576,997,242496).
Variants include:
<<1>> P.: I do not know your sum.
<<2>> S.: Thanks for that information.
<<3>> P.: I still don't know your sum.
<<4>> S.: Now I know your product.
<<5>> P.: And now I know your sum.
S=8 and P=16 is a solution
for this puzzle.
Scenario III:
<<1>> P.: I do not know your sum.
<<2>> S.: Thanks for that information.
<<3>> P.: I still don't know your sum.
<<4>> S.: Thanks for that information.
<<5>> P.: Thanks for that information.
<<6>> S.: Now I know your product.
<<7>> P.: And now I know your sum.