Mathematics Stack Exchange
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Questions tagged [cryptarithm]

A cryptarithm is a numeric puzzle in which a mathematical equation is given where the digits are replaced by letters, the object being to recover the original equation. The canonical example is SEND + MORE = MONEY, which has the unique solution 9567 + 1085 = 10652. There are variants, such as long division problems where most of the digits are replaced by asterisks.

A cryptarithm is a numeric puzzle in which a mathematical equation is given where the digits are replaced by letters, the object being to recover the original equation. The canonical example is SEND + MORE = MONEY, which has the unique solution 9567 + 1085 = 10652. There are variants, such as long division problems where most of the digits are replaced by asterisks.

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Solving $DEF+FEF=GHH$, $KLM+KLM=NKL$, $ABC+ABC+ABC=BBB$

She visits third class and is $8$ years old (you can imagine how ashamed I felt when I said so to her). I helped her with lots of maths stuff today already but this is very unknowable for me. Sorry it's in German but I have translated it :) It's…
cnmesr
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Christmas Cryptarithm: "HERES+MERRY+XMAS=READER"

I got this puzzle from some others: \begin{array}{c c c c c c}&\mathrm H&\mathrm E&\mathrm R&\mathrm E&\mathrm S\\&\mathrm M&\mathrm E&\mathrm R&\mathrm R&\mathrm Y\\+&&\mathrm X&\mathrm M&\mathrm A&\mathrm S\\\hline\mathrm R&\mathrm E&\mathrm…
Simply Beautiful Art
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A number 47_ _74 is a multiple of consecutive numbers. Find the numbers.

I had recently solved a problem. A number 47_ _74 is multiple of at least two consecutive numbers. Find the numbers. The list of numbers may be of any length $\ge 2$. I first saw that if they were multiples of 4 numbers then it must be divisible…
TheRandomGuy
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Alphametics Question

In the figure below, each distinct letter represents a unique digit such that the arithmetic sum holds. If the letter L represents 9, what is the digit represented by the letter T? TERRIBLE + NUMBER ========== THIRTEEN I know I…
snivysteel
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A cryptogram Diophantine $\overline{ABCDE}=4 \ \overline{AB}^2+\overline{CDE}^2$

ABCDE is a 5-digit number. AB and CDE are 2-digit and 3-digit numbers respectively. $\overline{ABCDE}=4 \ \overline{AB}^2+\overline{CDE}^2$ Find all possible values of $\overline{ABCDE}$. Honestly, I designed this problem just for fun, and I tried…
Ghartal
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Solving the cryptarithm "THE+BEST+SYSTEM=METRIC"

I came across a question that I couldn't figure out. It was: What is the value of all the letters in this following cryptarithm? $$\begin{array}{ccccccc} &&&&T&H&E\\ +&&&B&E&S&T\\ &S&Y&S&T&E&M\\ \hline &M&E&T&R&I&C\\ \end{array}$$ The problems I…
Stevo
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$MATHS\times7=POISON$ where $MATHS$ is a prime

Today, when I was doing a past paper for my upcoming competition, I found a interesting but hard problem: In the equation below, each letter represents distinct digits from $0$ to $9$. $$MATHS\times7=POISON$$Where the five-digit number $MATHS$ is…
Culver Kwan
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Algorithm (cryptarithm) question, yes it is homework, but I can't get it

The following is a multiplication problem in traditional base ten notation. Each letter represents a different digit. What digit does each letter represent? How did you get your foot in the door?
NEWprogrammer
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The sum of the two 7-digit numbers CARIBOU and CARIBOO is 3456789. What is C+A+R+I+B+O+U?

I got this question from a math contest, and I need to know how to find the following. I am rather new to cryptarithms, and I really need to master that skill. For the contest, I needed to find out the following: If $CARIBOU+CARIBOO=3456789$ find…
ShadowKnight700
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Quickly finding $(-M)^{ATH}$ from $M+A+T+H=10$, $M-A+T+H=6$, $M+A-T+H=4$, $M+A+T-H=2$

I found this question on social media, from a math account I follow. $$\begin{align} M+A+T+H &=10 \\ M-A+T+H &=\;6 \\ M+A-T+H &=\;4 \\ M+A+T-H &=\;2 \\ (-M)^{ATH} &=\;\text{??} \end{align}$$ To solve this I set up an augmented matrix that looked…
AllCatsAreGrey
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Solving for the digits in WHITE+WATER=PICNIC

I'm writing solutions for students who are taking a competition exam and I took problems from old purple comet competition problems. This problem is the last one from the 2004 middle school contest and says: In the addition problem…
teenytones
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Solving the cryptarithm $\mathrm{TWO}+\mathrm{TWO}=\mathrm{FOUR}$ in base $10$ and base $7$

Find the numerical value of each of the letters in the following expression $$\mathrm{TWO}+\mathrm{TWO}=\mathrm{FOUR}$$ in (a) base $10$ and (b) base $7$. I don't even know how I would approach this problem. Any help would be appreciated.
Toshu
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How to solve this alphametic (verbal arithmetic)?

I know I can get the answer for this puzzle but I'm struggling to see how to solve it. Every letter represents a different number (0-9): PLAYS + WELL ======= BETTER So far I know that: B = 1 (has to be) P = 9 (because P + 1 ≥ 10) E =…
tempy
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How do I solve this number theory question?

Question Sherlock Holmes and Dr. Watson recover a suitcase with a three-digit combination lock from a mathematician turned criminal. Embedded in the suitcase above the lock is the cryptic message "AT SEA BASE. SEAS EBB SEA: BASS. " Dr. Watson…
HI1915
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Code intercepted - BLASE+LBSA=BASES. Can there be two solutions?

This question is from the book 'Mathematical Circles', and it goes like this: The secret service of The Federation intercepted a coded message from the Dominion which read: BLASE + LBSA = BASES. It is known that equal digits are coded with equal…
Pumpkin_Star
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