\section*{Problem 6 - V01206}

Which digit stands in the units place of the sum

\[
11^{6}+14^{6}+16^{6}
\]
}

Since we are only interested in the units place of the summands, we follow \(\bmod 10\)

\[
\left(11^{6}+14^{6}+16^{6}\right) \quad \bmod 10 \equiv\left(1^{6}+4^{6}+6^{6}\right) \quad \bmod 10
\]

It is \(4^{6}=4096\), so \(4^{6} \bmod 10 \equiv 6 \bmod 10\) and it is \(6^{6}=6^{3} \cdot 6^{3}=216 \cdot 216\), so \(6^{6} \bmod 10 \equiv 6\) mod 10. Therefore,

\[
\left(11^{6}+14^{6}+16^{6}\right) \quad \bmod 10 \equiv 13 \quad \bmod 10 \equiv 3 \quad \bmod 10
\]

and thus the sum ends with the units digit 3.