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Math and Logic

Wows and Meows

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.

1B+B671 \Large \begin{array} { c c c } & 1 & \red{B} \\ + & \red{B} & 6 \\ \hline & 7 & 1 \\ \end{array}

What digit in place of B\red{B} would make this sum true?

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

Hence, B \red{B} =5:= 5:

15+5671 \Large \begin{array} { c c c } & 1 & \red{5} \\ + & \red{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?

BA×616A \Large \begin{array} { c c c } & \green{B} & \pink{A} \\ \times & & 6 \\ \hline 1& 6 & \pink{A} \\ \end{array}

Since we know that the product is a multiple of 6,6, it must be both even and divisible by 3.3. Therefore, the only final digits possible are 22 and 8:8: we can't have an odd final digit because then the number wouldn't be even, and we can't have 0,4,0, 4, or 66 because then we'd have a number that's not divisible by 3.3.

So we have two possibilities: B2×6=162 \green{B} 2 \times 6 = 162 or B8×6=168. \green{B} 8 \times 6 = 168. However, 162=6×27162 = 6 \times 27, so the first option won't work. What about the second? Well, 168=6×28168 = 6 \times 28, so that must be the answer: A=8A = 8 and B=2B=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.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 10.10.

  • 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

In this cryptogram, different letters correspond to different digits, and leading digits cannot be 0.0.

What digit is E?\green{E}?

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