What is the remainder when $2^{2024}$ is divided by 3?

$2^{1} \equiv 2$, $2^{2} \equiv 1$, $2^{3} \equiv 2$, $2^{4} \equiv 1 \pmod{3}$. Since 2024 is even, $2^{2024} \equiv 1 \pmod{3}$.