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## Let the Lass

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 if different letters are used, the digits are also different.

Keep reading to see a couple example puzzles, or dive right into today's challenge.

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

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

Looking at the last column, we have that $\color{#EC7300}{B}$ $+ 6$ ends in a $1,$ so we must have $\color{#EC7300}{B}$ $= 5$. Checking the rest of this cryptogram, we verify that $15 + 56 = 71$ is true!

Hence, $\color{#EC7300}{B}$ $= 5:$

$\Large \begin{array} { c c c } & 1 & \color{#EC7300}{5} \\ + & \color{#EC7300}{5} & 6 \\ \hline & 7 & 1 \\ \end{array}$

Not all cryptograms unravel in a single step like the one above. For example, consider divisibility rules — what numbers can multiply together to make a specific product?

$\Large \begin{array} { c c c } & \color{#20A900}B & \color{#D61F06}A \color{#333333}\\ \times & & 6 \\ \hline 1& 6 & \color{#D61F06}A\color{#333333} \\ \end{array}$

Since we know that the product is a multiple of $6,$ it must be both even and divisible by $3.$ Therefore, the only final digits possible are $2$ and $8:$ we can't have an odd final digit because then the number wouldn't be even, and we can't have $0, 4,$ or $6$ because then we'd have a number that's not divisible by $3.$

So we have two possibilities: $\color{#20A900}B\color{#333333}2 \times 6 = 162$ or $\color{#20A900}B\color{#333333}8 \times 6 = 168.$ However, $162 = 6 \times 27$, so the first option won't work. What about the second? Well, $168 = 6 \times 28$, so that must be the answer: $A = 8$ and $B=2$.

Here are a couple more advanced techniques to consider:

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

• Carry digits: Be aware of how carry digits work — when adding two numbers, you carry the ‘overflow’ from one place value to the next if the sum is greater than or equal to $10.$

• Check cases: Organize and eliminate possibilities — keeping track of the possibilities carefully and in an organized way!

Now try your hand at the cryptogram below.

# Today's Challenge

If the same letter is used twice, it’s the same digit in both places, and if different letters are used, the digits are also different.

No number is written with a leading zero. For example, $53$ cannot be written as $053.$

$\Large \begin{array} { c c c c } & \color{#D61F06} L & \color{#69047E} E & \color{#3D99F6} T \\ + & \color{#3D99F6} T & \color{#20A900} H & \color{#69047E} E \\ \hline \color{#D61F06} L & \color{#333333} A & \color{#EC7300} S & \color{#EC7300} S \\ \end{array}$

This puzzle has multiple solutions. Which letter represents the same digit in all solutions? Select all that apply. Select one or more

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