1. What is the unit digit of the number $2023^{\left(2022^{2021}\right)}$ ?
$\begin{array}{ll}\text { (A) } 3 & \text { (B) } 9\end{array}$
(C) 7
(D) 1
(E) 5
Problem 1. The correct answer is (D).

Since $3^{4}=81$, if $n$ is any multiple of 4, the units digit of $3^{n}$ is 1. The same will be true for any $t^{n}$, if $t$ is a natural number where the units digit is 3. Since the exponent of 2023 in the given expression, namely $2022^{2021}$, is a multiple of 4, it follows that the required digit is 1.