1. Using the digits $4,5,6,7,8$ and 9, a six-digit number was written. Zoran, Darko, and Nikola guessed the number. Zoran: 574698, Darko: 786945, Nikola: 456789. It turned out that Zoran correctly guessed the positions of three digits. Darko also guessed the positions of three digits, and Nikola guessed the position of only one digit. Determine the six-digit number.
Solution. Zoran, Darko, and Nikola made the following guesses for the unknown number:

| Zoran: | 5 | 7 | 4 | 6 | 9 | 8 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| Darko: | 7 | 8 | 6 | 9 | 4 | 5 |
| Nikola: | 4 | 5 | 6 | 7 | 8 | 9 |

We observe that the guesses of Zoran and Darko do not match in any digit. Since each of them guessed three digits correctly, it follows that these are three different digits. Therefore, the digit that Nikola guessed must be in the same position as either Zoran or Darko. We see that this can only be the digit 6. This means that Darko guessed the digit 6, so Nikola did not guess this digit. Therefore, the fourth position is correct according to Darko, i.e., the fourth digit is 9. By similar reasoning, we conclude that Darko guessed the third, fourth, and fifth digits correctly, while Zoran guessed the first, second, and sixth digits correctly. Therefore, the desired number is 576948.