### Mathematical Fundamentals

$\Large \begin{array} { c c c } & 1 & \color{#EC7300}{B} \\ + & \color{#EC7300}{B} & 6 \\ \hline & 7 & 1 \\ \end{array}$

Cryptograms are puzzles where capital letters stand in for the digits of a number. If the same letter is used twice, it’s the same digit in both places. And, in all of our puzzles, different letters represent different digits.

Solve enough cryptograms, and you’ll start to see patterns — tricks that will help you solve puzzles like these faster and more skillfully.

# Cryptograms

$\Large \begin{array} { c c c } & 1 & \color{#EC7300}{B} \\ + & \color{#EC7300}{B} & 6 \\ \hline & 7 & 1 \\ \end{array}$

What digit in place of $\color{#EC7300}{B}$ would make this sum true?

# Cryptograms

$\large \begin{array} { l l l l } & & \color{#20A900}{Z} & \color{#20A900}{Z} \\ & & \color{#20A900}{Z} & \color{#20A900}{Z} \\ & & & \color{#20A900}{Z} \\ & & & \color{#20A900}{Z} \\ +& & &\color{#20A900}{Z} \\ \hline & 1 & 0 & 0 \end{array}$ What digit is ${\color{#20A900}{Z}}?$

# Cryptograms

The remainder of the problems in this quiz get increasingly difficult as you go along. You will be called on to use all of the strategies below methodically and deliberately to work out solutions:

• Converting the problem into equations that take the place values of the letters into account. For example, $R2D2 = 1000R + 200 + 10D + 2.$

• Keeping track of how carrying the overflow from one place value to the next if the sum is greater than or equal to 10 impacts the cryptogram.

• Keeping track of all of the possibilities carefully and in an organized way so that you remember what you've ruled out and what's still possible.

Which of these techniques did you already use while solving the two previous warmup puzzles?

# Cryptograms

$\Large \begin{array} {c c c c } & & \color{#D61F06}{A} & \color{#3D99F6}{B} \\ + & & \color{#D61F06}{A} & \color{#3D99F6}{B} \\ \hline & 1 & 3 & 8 \\ \end{array}$

What is the value of $\color{#D61F06}{A} \color{#333333}{?}$

# Cryptograms

$\Large \begin{array} {c c c } & 1 & \color{#3D99F6}{E} \\ \times & & \color{#3D99F6}{E} \\ \hline & 9 & \color{#3D99F6}{E} \\ \end{array}$

What digit in place of $\color{#3D99F6}{E}$ would make this multiplication true?

# Cryptograms

$\def\arraystretch{1.5} \begin{array} {ccccc} \large & & & & \large \color{#69047E}{X}& \large \color{#69047E}{X}\\ \large & & & & \large \color{#D61F06}{Y}& \large \color{#D61F06}{Y}\\ \large + & & & & \large \color{#3D99F6}{Z}& \large \color{#3D99F6}{Z}\\ \hline \large& & & \large \color{#69047E}{X} & \large \color{#D61F06}{Y} & \large \color{#3D99F6}{Z} \end{array}$

If each letter represents a different nonzero digit, what must $\large \color{#3D99F6}{Z}$ be?

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