Find two numbers based on their sum/difference

Computer Science Level 4

Two logicians must find two distinct integers \(A\) and \(B\) such that they are both between 2 and 100 inclusive, and \(A\) divides \(B\). The first logician knows the sum \( A + B \) and the second logician knows the difference \(B-A\).

Then the following discussion takes place:

  • Logician 1: I don't know them.
  • Logician 2: I already knew that.
  • Logician 1: I already know that you are supposed to know that.
  • Logician 2: I still can't figure out what the two numbers are.
  • Logician 1: Oops, I think I misestimated my last conclusion; I didn't know that yet!

Enter your answer as a decimal number \(A.B\). (For example, if \(A=23\) and \(B=92\), write \(23.92\).)


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