\section*{Problem 1 - 261011}

What is the last digit of the number

\[
z=4444^{444^{44^{4}}} ?
\]
}

The powers of 4444 end with the same digit as the same powers of 4. These end in 6 if the exponent is even, and they end in 4 if the exponent is odd. The exponent

\[
n=444^{44^{4}}
\]

is an even number, since \(n\) itself is a power whose base is even. Therefore, \(z=4444^{444^{44^{4}}}\) ends in 6.