Which is the smallest positive integer divisible by 28, whose decimal representation ends in 28, and the sum of whose digits is 28?
Let the sought number be $100 B+28$. Clearly, $100 B$ is also divisible by 28, meaning $B$ is divisible by 7; furthermore, since the sum of the digits of $B$ is $28-(2+8)=18$, $B$ is also divisible by 9, hence it is a multiple of 63. Some multiples of 63: $63, 2 \cdot 63=126$, $3 \cdot 63=189, \ldots$ It can be seen that the smallest among these where the sum of the digits is 18 is 189. Therefore, the smallest number that satisfies the conditions is $189 \cdot 100+28=18928$.