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.

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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 ...
teenytones's user avatar
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1 answer
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Alphanumeric Puzzle multplication : $OW\times HE=WWW$ [closed]

$OW\times HE=WWW$ where $O,W,H,E$ are digits. I've gathered that $$W\in\{2,3,4,5,6,7,8,9\}$$ $$E\in\{1,3,6,7,9\}$$ but I can't seem to move past it.
yourfuckly's user avatar
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1 answer
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Why first letter of a word in cryptarithmetic problem can't be 0?

I was given a cryptarithmetic problem by my teacher: $$\mathrm{TWO}+\mathrm{TWO}=\mathrm{FOUR}$$ I solved it as F=0, O=2, U=6, R=4, T=1 and W=3. $$\begin{array}{ccccccc} &&&&1&3&...
sanyam's user avatar
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Studying diophantine magic squares

A bit of context I'm analyzing a type of cryptarithmetic puzzle that consist in the simultaneous resolution of 6 cryptarithms arranged in a magic square fashion. Here's an example: Solution: My goal ...
Domenico Modica's user avatar
4 votes
2 answers
107 views

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 ...
Ghartal's user avatar
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2 votes
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115 views

General Approach to Solving Cryptarithms [closed]

I have recently started honing my problem-solving skills, starting with number-related problems. Cryptarithms have appeared frequently, so I was wondering whether there is some sort of general ...
Developer's user avatar
1 vote
2 answers
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Solve alphanumeric puzzle $(HE) \times (EH) = (WHEW).$

This is a self-answer query. I came across a recent mathSE query that presented an interesting problem, and took some time solving it. When I looked for the query to respond, I couldn't find it. I ...
user2661923's user avatar
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How to find $\overline{abc}_{7}-\overline{cba}_{7}=\overline{xy4}_{7}$?

The problem is as follows: Let: $\overline{abc}_{7}-\overline{cba}_{7}=\overline{xy4}_{7}$ Assuming $a=b-c$ Find: $cba_{7}$ in terms of decimal system. How exactly should I do this?. Can someone ...
Chris Steinbeck Bell's user avatar
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1 answer
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What's the value of two digits from a certain number composed by six digits when it comes from a prime?

The problem is as follows: The number $\overline{ab0ab0}$ is the result of the product between two consecutive prime numbers. Assuming the $0$ in the number represents zero. Find the value of $\...
Chris Steinbeck Bell's user avatar
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1 answer
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How to find the base number of of two number systems when there's a difference in the quanity of numbers?

The problem is as follows: In two numbering systems which are of consecutive bases, there are about $120$ three-digit numerals more than the other. Find the smallest of these bases. The alternatives ...
Chris Steinbeck Bell's user avatar
0 votes
1 answer
44 views

How to find the values which would equate the division between two numbers of swapped digits without knowing anything further? [duplicate]

I'm having difficulty in assess this problem in a method without relying too much in too many trial and error. I have noticed there is a similar puzzle but in such it includes the value of one of the ...
Chris Steinbeck Bell's user avatar
0 votes
1 answer
51 views

How to find the number of marbles which someone has when it is a multiple of an unknown number?

The problem is as follows: Mark has $\overline{ab}$ marbles and Ferdinand has $\overline{cde}$ marbles. Find the total of marbles which both have knowing that the product of the number of marbles ...
Chris Steinbeck Bell's user avatar
3 votes
2 answers
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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 ...
Crocogator's user avatar
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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\\ +&&...
Stevo's user avatar
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1 answer
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What number the letter O represents in this cryptarithm? [closed]

I found a question and I do not know how to do it. The goes as: If letters all represent digits, what is the value of O in: $$\begin{array}{ccccccc} &&&&O&N&E\\ +&&&...
Stevo's user avatar
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15 votes
4 answers
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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&\...
Simply Beautiful Art's user avatar
1 vote
2 answers
116 views

Eight distinct integer values between $1$ and $8$ satisfy six simple conditions ($D+E=F$, etc). Find which value is which.

I have 8 variables; $A$, $B$, $C$, $D$, $E$, $F$, $G$, and $H$. What are they all equal to? Rules: All the variables are equal to integer values between one and eight. None of the variables are ...
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How to find the value of 5 variables

I have an equation: $$O^R-C+K^Y=ROCKY$$ All of the variables are whole numbers from $0$ to $9$ inclusive. There cannot be any duplicate numbers. I need to find the value of all of the variables.
RedGuy11's user avatar
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The question in the school magazine : $DBSPD-WILL=WIN$

When I was reading my school magazine, I found some hard problems in the Math Corner page. I can't solve two of the questions. Here is one of them In the equation below, each letter represents ...
Culver Kwan's user avatar
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3 votes
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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=...
Culver Kwan's user avatar
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3 answers
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Help solving a digit and word code problem/riddle: sum of four "ONE"s is "TEN"

Replace each letter by a digit. The same digit must represent each letter, and no beginning letter of a word can be zero. No two letters can be the same number. Find the digits represented by the ...
italy's user avatar
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2 answers
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How did we know that X must be equal to 1? [closed]

I did not understand the solution to this problem
Devansh Arora's user avatar
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2 answers
80 views

Multiplication Question

I have this question for my math class. I've been working on it for about an hour. Here it is: Each of the letters, F,I,V,E, in this multiplication stands for a different digit. What are the values ...
TheSaint321's user avatar
1 vote
1 answer
85 views

If $a,b,c\in N$, such that $aaaaaa=b*c*bc*(b+b+c)*(c+c-b)(c-b)$, then find $a,b,c$.

If $a,b,c\in N$, such that $aaaaaa=b*c*bc*(b+b+c)*(c+c-b)(c-b)$, then find $a,b,c$. Where $aaaaaa$ is a six digit no. with each digit equal to $a$ and $bc$ is a 2-digit no. with digits $b$ and $c$. I ...
ami_ba's user avatar
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73 votes
15 answers
19k views

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'...
cnmesr's user avatar
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Find the digit represented by C.

I am self-studying Multiplication and Division. This is a problem I encountered and have hard time with it. I have no clue where to start. In fact, I have read this problem many times, wondering ...
math's user avatar
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2 answers
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An arithmetic puzzle

My answer for this problem is far from that given by the answer sheet. In the multiplication $abcde \times e=edade$, each letter represents a different digit. what digit does the letter C represent?...
math's user avatar
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-2 votes
1 answer
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Is there an encryption scheme that provides $Pr\{M_1 = m_1\wedge M_2 = m_2 | C_1 = c_1 \wedge C_2 = c_2\} = Pr\{M_1 = m_1 \wedge M_2 = m_2\}$

Question: Consider the following definition of perfect secrecy for the encryption of two messages.An encryption scheme (Gen, Enc, Dec) over a message space M is perfectly-secret fortwo messages if ...
Mohammad Rostami's user avatar
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2 answers
8k views

Solving an algorithm math problem

if x, y and z each represent a different digit from 0 to 9, what is the value of (x)(y)(z)? 4z 27 +x5 ____ y14 I answered it like this: ...
Alicia's user avatar
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7 votes
1 answer
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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 ...
TheRandomGuy's user avatar
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0 votes
2 answers
265 views

Maths for the Diffie Hellman

With respect to the maths behind the Diffie Hellman Key exchange algorithm. Why does: (ga mod p)b mod p = gab mod p It might be fairly obvious, but what basic maths guarantees this? Why does the ...
user3742467's user avatar
2 votes
2 answers
1k views

Cryptarithm - Interesting Math Problem

This is a very interesting cryptarithm that I came across in an old textbook of mine. It is named accordingly as a tribute to the late Bob Marley (singer). Cryptarithm - Tribute to Bob Marley In the ...
anonymous's user avatar
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0 votes
1 answer
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Solving cryptarithmetic problems

I was recently trying to solve cryptarithmetic problems like: F Y H * E W T -------- Z E T F E K Z Z Y Z T X ------------ Y F Y W E F ...
user1369975's user avatar
4 votes
1 answer
2k views

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? ...
snivysteel's user avatar
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1 answer
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help me to solve this Cryptarithm problem

Hello I tried various things but ain't getting where to begin, if anybody would let me know how to solve this it will be of great help P X B * W Y A        &...
user2032986's user avatar
1 vote
1 answer
226 views

How to begin solving this cyrptarithm?

Anybody please help me in how to begin with this cryptarithm. I tried to find for 0,1,5,6,9 but none of them are clearly recognizable.. o u i * o u i ...
user2032986's user avatar
0 votes
1 answer
493 views

How to solve a cryptarithm with multiple conditions

I'm trying to solve a cryptarithm that must meet all of the following conditions: one + one = two seven is prime nine is a perfect square More specifically, i'm trying to find the ...
user72364's user avatar
  • 101
2 votes
1 answer
2k views

How to solve multiplication alphametics?

I am referring to puzzles like these, where every letter represents a unique number (0-9): ...
tempy's user avatar
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3 votes
1 answer
9k views

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): ...
tempy's user avatar
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2 votes
1 answer
119 views

What is the base for the following number system?

So there was a spaceship sent back with the following picture that assumed to constitute an addition. What is the base of the number system? ...
A_1_615's user avatar
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1 vote
3 answers
4k views

How to solve a cryptarithm?

Given multiplication is $$\begin{array}{cccccc} & & & P & E & N \\ & & & I & N & K \\\hline & & L & K & P & R \\ & ...
Vivek Goel's user avatar
4 votes
2 answers
3k views

Algorithm (cryptarithm) question, yes it is homework, but I can't get it [closed]

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's user avatar
2 votes
2 answers
2k views

(PQ)²=RSP, where P,Q,R,S are distinct single digit natural numbers, then R=?

I have a problem I tried to solve, but couldn't because I don't know the method to solve it and I've never come across such problem. Here's the problem. $(PQ)²=RSP$ Where $P, Q, R, S$ are distinct ...
Electrifyings's user avatar