Kirienko D:

Sasha and Masha each thought of a natural number and told them to Vasya. Vasya wrote the sum of the numbers on one sheet of paper and their product on another, then hid one of the sheets and showed the other (which had the number 2002 written on it) to Sasha and Masha. Seeing this number, Sasha said that he did not know what number Masha had thought of. Hearing this, Masha said that she did not know what number Sasha had thought of. What number did Masha think of?
Both guessed divisors of the number 2002 (otherwise someone would have understood that 2002 is the sum of the guessed numbers and determined the second number). However, even knowing that Sasha guessed a divisor, Masha cannot rule out that 2002 is the sum. But the sum of divisors equals 2002 only in the case of 1001 + 1001 (other divisors are 2002 or less than 1001). Therefore, Masha guessed 1001 (and Sasha guessed 2 or 1001, and then both really could not have known each other's numbers).

## Answer

1001.