10. (10 points) $n$ pirates divide gold coins. The 1st pirate takes 1 coin first, then takes $1 \%$ of the remaining coins; then, the 2nd pirate takes 2 coins, then takes $1 \%$ of the remaining coins; the 3rd pirate takes 3 coins, then takes $1 \%$ of the remaining coins; ... the $n$-th pirate takes $n$ coins, then takes $1 \%$ of the remaining coins. As a result, all the gold coins are divided, and each pirate gets the same number of coins. How many gold coins are there in total? $\qquad$ .
【Solution】Solution: According to the problem, we know:
The $n$-th pirate takes $n$ coins first, then takes 1% of the remaining, and the coins are all taken. This means the remaining coins are 0. The $n$-th pirate actually took $n$ coins.

The $n$-1-th pirate takes $n-1$ coins first, then takes 1% of the remaining. Since each pirate takes the same amount, the 1% of the remaining coins is 1 coin, so the remaining 99% is 99 coins. Therefore, $n=99$, each person takes 99 coins, and there are 99 people.
$$
99 \times 99=9801 \text {. }
$$

Therefore, the answer is: 9801.