# 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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