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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In the addition $\begin{array}{c|c|c}+ A \ A\ A \\ \ \ B\ B\ B \\ \hline A \ A\ A\ C \end{array}$, $A,B,C$ each denotes a digit. Find them.
In the addition $\begin{array}{c|c|c}+ A \ A\ A \\ \ \ B\ B\ B \\ \hline A \ A\ A\ C \end{array}$, $A,B,C$ each denotes a digit. Find them.
The solution says, "First of all $A$ denotes $1$ ...
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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 ...
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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.
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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&...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $\...
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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 ...
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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 ...
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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 ...
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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}$$
in (a) base $10$ and (b) base $7$.
I don't even know how I would approach this ...
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Solving the cryptarithm "THE+BEST+SYSTEM=METRIC"
I came across a question that I couldn't figure out. It was:
What is the value of all the letters in this following cryptarithm?
$$\begin{array}{ccccccc}
&&&&T&H&E\\
+&&...
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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:
$$\begin{array}{ccccccc}
&&&&O&N&E\\
+&&&...
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Christmas Cryptarithm: "HERES+MERRY+XMAS=READER"
I got this puzzle from some others:
\begin{array}{c c c c c c}&\mathrm H&\mathrm E&\mathrm R&\mathrm E&\mathrm S\\&\mathrm M&\mathrm E&\mathrm R&\mathrm R&\...
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Eight distinct integer values between $1$ and $8$ satisfy six simple conditions ($D+E=F$, etc). Find which value is which.
I have 8 variables; $A$, $B$, $C$, $D$, $E$, $F$, $G$, and $H$.
What are they all equal to?
Rules:
All the variables are equal to integer values between one and eight.
None of the variables are ...
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How to find the value of 5 variables
I have an equation:
$$O^R-C+K^Y=ROCKY$$
All of the variables are whole numbers from $0$ to $9$ inclusive. There cannot be any duplicate numbers. I need to find the value of all of the variables.
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The question in the school magazine : $DBSPD-WILL=WIN$
When I was reading my school magazine, I found some hard problems in the Math Corner page. I can't solve two of the questions. Here is one of them
In the equation below, each letter represents ...
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$MATHS\times7=POISON$ where $MATHS$ is a prime
Today, when I was doing a past paper for my upcoming competition, I found a interesting but hard problem:
In the equation below, each letter represents distinct digits from $0$ to $9$. $$MATHS\times7=...
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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 ...
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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
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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 ...
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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 ...
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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'...
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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 ...
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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?...
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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 ...
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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:
...
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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 ...
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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 ...
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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 ...
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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
...
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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?
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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
&...
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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
...
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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 ...
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How to solve multiplication alphametics?
I am referring to puzzles like these, where every letter represents a unique number (0-9):
...
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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):
...
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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?
...
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How to solve a cryptarithm?
Given multiplication is
$$\begin{array}{cccccc}
& & & P & E & N \\
& & & I & N & K \\\hline
& & L & K & P & R \\
& ...
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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?
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(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 ...
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