\[ \begin{array} {ccccc} \huge & & & & \huge \color{purple}{X}& \huge \color{purple}{X}\\ \huge & & & & \huge \color{red}{Y}& \huge \color{red}{Y}\\ \huge + & & & & \huge \color{blue}{Z}& \huge \color{blue}{Z}\\ \hline \huge& & & \huge \color{purple}{X} & \huge \color{red}{Y} & \huge \color{blue}{Z} \end{array} \]

**If each letter represents a different nonzero digit, what must \(\large \color{blue}{Z}\) be?**

Solve this your own way and then check out the solutions -- there are at least two very different approaches for solving this one!

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