Logic
# Cryptograms

\[ \begin{array}{ccccc} & & & & A&B\\ \times & & & & &9 \\ \hline & & & C & 2 &3 \end{array} \]

Use the divisibility rules of 9 to find the value of \(C\).

\[ \begin{array} { l l l l }

& & & & \ 9 \\
\times & & & 3 & X \\
\hline
& & 3 & 3 & 3 \\
\end{array} \]

What digit \(X\) satisfies the cryptarithm above?

\[ \large{\begin{array}{ccccccc} && & & & & 5& P \\ \times && & & & &Q &R\\ \hline & & & & & 8& 0&0 \end{array}} \]

Knowing that \(800 = 2^5\times5^2\), find the value of the 2-digit integer \(\overline{QR}\).

\[ \large{\begin{array}{ccccccc} && & & & & 4& E \\ \times && & & & & 2&1 \\ \hline & & & & & F & 4 & 5 \end{array}} \]

Determine the value of \(F\).

\[ \large{\begin{array}{ccccccc} && & & & & & E \\ \times && & & & & &E \\ \hline & & & & & & 3 & E \end{array}} \]

Find the value of \(E\).

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