A number, when divided by 7, gives a remainder of 2, and when divided by 8, gives a remainder of 4. In the former case, the quotient is 7 greater than in the latter case. What is the number?
Let the quotient when divided by 7 be $x$. Since the remainder of the division is 2, the number we are looking for is $7 x+2$. In the case of division by 8, the quotient is $x-7$ according to the problem, and the remainder is 4. Thus, the number can also be written as $8(x-7)+4$. The two forms are equal:

$$
7 x+2=8(x-7)+4
$$

From this,

$$
x=54
$$

and thus the number we are looking for is

$$
7 \cdot 54+2=380
$$

Károly Huszár (Kaposvár, Táncsics g. II. o. t.)