The 5774 Ulpaniada (part 2 of it, which was taken yesterday) includes the following question:
How many three digit numbers are there which are equal to $34$ times the sum of their digits?
It offers five choices: $10$, $8$, $6$, $4$, and $0$.
I don't want to check the sums of digits of $3\times34,4\times34,\ldots,29\times34$ (all the three-digit products). There must be a better method: any suggestions?