IMAS 2020–2021 Junior Division — First Round Question 20

Question 20

Given a four-digit integer $\overline{abcd}$ and a positive integer $k$ which satisfies $\overline{abcd}=k(a+b+c+d)^2$, what is the minimum value of $k$?

$32$
$13$
$12$
$4$
$3$