MathNet 2024-part-06 — 165 problems (EN–VI) Question 41

Positive integers $a$, $b$, and $c$ have the property that $a^{b}$, $b^{c}$, and $c^{a}$ end in $4$, $2$, and $9$, respectively. Compute the minimum possible value of $a+b+c$.