Logic

# Number Theory Techniques - 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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