9.4 In the thirtieth kingdom, there are three types of coins in circulation: bronze rubles, silver coins worth 9 rubles, and gold coins worth 81 rubles. From the treasury, which contains an unlimited supply of each type of coin, a certain amount was issued with 23 coins, which is less than 700 rubles. Find this amount, given that it is impossible to issue it with a smaller number of coins.
Solution. Since the issued amount is less than 700 rubles, the number of gold coins is less than $700: 81$, which means no more than 7. Then the number of bronze and silver coins together is at least $23-7=16$. Note that the number of bronze coins cannot exceed 8: otherwise, we can replace 9 bronze coins with 1 silver coin, and the method of issuing the amount would not be unique. Similarly, the number of silver coins is no more than 8. Therefore, there are exactly 8 of each, and 7 gold coins. The issued amount (in rubles) is $8 \cdot 1 + 8 \cdot 9 + 7 \cdot 81 = 647$.

Answer: 647 rubles.

| INCLUDED IN THE SOLUTION | SCORE |
| :--- | :---: |
| Correct and justified answer | 7 points |
| The correct answer is provided and it is shown that the amount of 647 rubles can be issued in a unique way. However, the uniqueness of this number is not demonstrated. | 4 points |
| It is proven that the number of bronze (or silver) coins issued is no more than 8 | 3 points |
| Correct but unexplained answer | 1 point |