Two students
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
and
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
are playing the following game: Each of them writes down on a sheet of paper a positive integer and gives the sheet to the referee. The referee writes down on a blackboard two integers, one of which is the sum of the integers written by the players. After that, the referee asks student
![A:](/media/m/3/e/4/3e48d6f77f001323ca55e54a34abdfee.png)
“Can you tell the integer written by the other student?” If A answers “no,” the referee puts the same question to student
![B.](/media/m/6/b/c/6bc9b0e17086ccf6fe102db1f5c3ebcf.png)
If
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
answers “no,” the referee puts the question back to
![A,](/media/m/8/6/5/865743fba196abcc2b01372b2f0205c1.png)
and so on. Assume that both students are intelligent and truthful. Prove that after a finite number of questions, one of the students will answer “yes.”
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Two students $A$ and $B$ are playing the following game: Each of them writes down on a sheet of paper a positive integer and gives the sheet to the referee. The referee writes down on a blackboard two integers, one of which is the sum of the integers written by the players. After that, the referee asks student $A:$ “Can you tell the integer written by the other student?” If A answers “no,” the referee puts the same question to student $B.$ If $B$ answers “no,” the referee puts the question back to $A,$ and so on. Assume that both students are intelligent and truthful. Prove that after a finite number of questions, one of the students will answer “yes.”