Task B-4.2. What is $49 \cdot 35$ if $49+35=82$?
Solution. It is obvious that the calculation is not performed in the decimal system, i.e.,

$$
49_{(x)}+35_{(x)}=82_{(x)}
$$

From $4 x+9+3 x+5=8 x+2$ we get that the base of the system is $x=12$. Then $49_{(12)}=57$ and $35_{(12)}=41$.

(2 points)

From $57 \cdot 41=2337$ and $2337=1429_{(12)}$, it follows that $49 \cdot 35=1429$ (in base 12).