4. Find the smallest four-digit number, the product of all digits of which is equal to 512.

Answer. 1888
Solution. $512=2^{9}$, which means all the digits of the number are powers of two, i.e., they can be $1, 2, 4$ or 8. Clearly, the first digit of the number should be as small as possible. Let's take the smallest of the possible ones, which is 1. The rest should be equal to 8, otherwise the product will be less than 512.

Criteria. Answer without justification (that this is the smallest number) - 1 point. Proven that the digits of the number can only be $1, 2, 4$ or 8 - 3 points.