21. Let's take any 1962-digit number divisible by 9. The sum of its digits will be denoted by $a$, the sum of the digits of $a$ by $b$, and the sum of the digits of $b$ by $c$. What is $c$?[^0]
21. Answer. $c=9$. The sum of the digits of any number gives the same remainder when divided by 9 as the number itself (PZ). On the other

![](https://cdn.mathpix.com/cropped/2024_05_21_7b8a6b2625543c3dae75g-113.jpg?height=438&width=322&top_left_y=1148&top_left_x=119)

Fig. 30 hand, $a \leqslant 1962.9<19999$, so $b \leqslant 1+4 \cdot 9=37$ and $c \leqslant 9$.