Logic
# Cryptograms

\[ \Large \begin{array} {c c c c }
& & \color{purple}{X}& \color{purple}{X} \\
& & \color{red}{Y} & \color{red}{Y} \\

+ & & \color{blue}{Z} & \color{blue}{Z} \\

\hline
& \color{purple}{X} & \color{red}{Y} & \color{blue}{Z} \\
\end{array} \]

If each letter represents a distinct digit, what is the value of the three-digit number \( \overline{XYZ}? \)

\[ \begin{array}{ccccc} & & & & A&B\\ \times & & & & A &A \\ \hline & & B & A & A &B \end{array} \]

Solve the above cryptogram. What is the first two-digit number in the product above, \(\overline{AB}\)?

Note: A number cannot start with 0, so A and B are non-zero.

\[ \begin{array} { l l l l l } & & & & & 9 & 9 & 9 \\ \times & & & & & A & B & C \\ \hline & & D & E & F & 1 & 3 & 2 \\ \end{array} \]

In this cryptogram, \(A,B,C,D,E\) and \(F\) are (not necessarily distinct) single digits. What is the value of \(A+B+C+D+E+F?\)

\[ \begin{array} { l l l l l } & S & E & N & D \\ + & M & O & R & E \\ \hline M & O & N & E & Y \\ \end{array} \]

In this cryptogram, each letter represents a distinct single digit positive integer except \(O\) which is equal to 0. Find the value of \(\overline{MONEY}.\)

\[ \large{\begin{array}{cccccc} & & & A & B & C&D\\ \times & & & & & &D\\ \hline & & & D& C & B&A\\ \end{array}} \]

Given that \(A,B,C\) and \(D\) are **distinct** single digit non-negative integers satisfying the cryptogram above, find \(A+B+C+D\).

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