András and Béla thought of a positive integer each, then they told the numbers to Csaba. Csaba informed them that the difference between the numbers was 1992. Then András told Béla that he did not know what number Béla had thought of. After some thought, Béla also told András that he did not know András's number. After this, András knew what number Béla had thought of, and even said that if they had both thought of the number one greater, he still wouldn't know Béla's number. What are the numbers they thought of?
Let the number thought of by András and Béla be $a$ and $b$, respectively. At the beginning of the game, András knew $a$, knew that $b$ was a positive integer and either $b=a-1992$ or $b=a+1992$; similarly, Béla knew that $a$ was a positive integer and either $a=b-1992$ or $a=b+1992$. Both of them had to choose the correct one from two possibilities.

I. Let's examine why András couldn't guess $b$ at first. If $a \leq 1992$, it would have been easy for András: $b=a-1992$ is not possible because $a-1992 \leq 0$, and $b$ is a positive integer. If, however, $a>1992$, then both $a-1992$ and $a+1992$ are positive integers, so in this case, András could not decide. Therefore, the reason András couldn't guess $b$ at first is that $a>1992$.

II. Then Béla started to think. Similarly, he realized that $a>1992$, but this information was not enough for him. Why? Because his number was greater than $2 \cdot 1992=3984$. If $b \leq 3984$, then $a=b-1992$ would not have been possible, since $b-1992 \leq 3984-1992=1992$. In this case, however, András and Béla would have guessed each other's number in the first round.

If, however, $b>3984$, then both $b-1992$ and $b+1992$ are greater than 1992, so Béla could not guess $a$.

The only reason, therefore, for Béla to "pass" was that $b>3984$.

III. The third time, András could have guessed Béla's number by excluding one of the cases between $b=a-1992$ and $b=a+1992$. Clearly, he also realized that $b>3984$, and this could have been enough for him because his number was not greater than $3 \cdot 1992=5976$.

If $a>5976$, then András could not have guessed Béla's number, because both $a-1992$ and $a+1992$ would have been greater than 3984. Thus, $a \leq 5976$, so András could exclude the case $b=a-1992$, because then $b=a-1992 \leq 3984$.

Therefore, András's number was not greater than 5976, and from this, he concluded that Béla's number was the larger one: $b=a+1992$.

IV. If both had thought of a number one greater, that is, András thought of $(a+1)$ and Béla thought of $(b+1)$, then

- András would not have guessed $(b+1)$ at first, because $(a+1)>1992$;

- Béla would not have been able to decide in the second round, since $(b+1)>3984$;

- András, according to his conclusion, would not have been able to decide in the third round either, so $(a+1)>5976$.

We have concluded that $a \leq 5976$, $b=a+1992$, and $(a+1)>5976$. This is only possible if $a=5976$ and $b=7968$.