How many times does 5 occur as a divisor in numbers ranging from 1 to 50000?
From 1 to 50000, there are 10000 numbers divisible by 5. Dividing these numbers by 5, the quotients will be:

$$
1,2,3, \ldots 10000
$$

Among these numbers, every fifth one is divisible by 5; thus, there are 2000 such numbers. Dividing them by 5 again, the quotients will be

$$
1,2,3, \ldots 2000
$$

Continuing this process, we see that 5 as a divisor appears:

$$
10000+2000+400+80+16+3=12493 \text{ times. }
$$

(Neidenbach Emil, Arad.)

The problem was also solved by: Bartók I., Dömény I., Haar A., Heimlich P., Jánossy Gy., Kertész G., Kiss J., Pám M., Pichler S., Schuster Gy., Schwemmer I., Szücs A.