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# Cryptograms

Cryptograms are puzzles where some (or all) digits are missing from an arithmetic operation. Tinker with different combinations of numbers and letters to unlock the right answer.

\[\Large \begin{array} {c c c } & \color{blue}A & \color{red}B & \color{orange}C \\ \times& & & 8 \\ \hline \color{blue}A & \color{orange}C & \color{orange}C & \color{orange}C \\ \end{array} \]

In the cryptogram above, \(A\), \(B\), and \(C\) are distinct digits. Find the value of \(A+B+C+8.\)

If \( A, B, C,\) and \(D\) are distinct digits, find the maximum possible value of the following sum:

\[ \begin{array} {ccc} & A & B \\ + & C & D \\ \hline \end{array} \]

\[\large{\begin{array}{lllllllll}&&&&&&&1&1&4&X&9\\\times&&&&&&&1&X&8&2&1\\\hline &\ &&1&2&3&4&5&6&7&8&9 \\\hline\end{array}}\]

Above shows an incomplete long multiplication for which X represents a single digit integer. What is the value of X?

Find

\[ \begin{array} { l l l } & & & X & Y & Z \\ & & & X & Y & Z \\ &+ & & X & Y & Z \\ \hline & & & Z & Z & Z \\ \end{array} \]

If \(X, Y,\) and \(Z\) are distinct digits, then what is the value of \(X \times Y \times Z ?\)

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