Questions tagged [alphametic]

Alphametic puzzles involve equations where digits have been replaced with letters, where the goal is usually to reconstruct the original equation, matching letters to numbers.

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12
votes
6answers
4k views

A four digit number using exact same 4 digits

ABCD is a 4 digit number where A,B,C and D are 4 distinctly separate digits between 1 and 9. Using any of the following math operations and the digits A,B,C and D exactly once get the number ABCD. ...
1
vote
0answers
124 views

General Approach to Solving Cryptarithms

I have recently started honing my problem-solving skills, starting with number-related puzzles. Cryptarithms have appeared frequently, so I was wondering whether there is some sort of general approach ...
16
votes
2answers
3k views

If O^3=DAD and (IM)^2=MOM, then what is MAID?

If $O^3=DAD$ and $(IM)^2=MOM$, then what is $MAID$? Source: Taken from the book Neurone Abaro Onuronon by Muhammad Zafar Iqbal.
4
votes
1answer
288 views

Multiplying English numbers is strange too

It seems that the English-speaking people multiply the numbers in the very same way that the Portuguese add them: while the latter say that 2+2=8, the former claim that 2×2 is 8: ...
10
votes
1answer
434 views

A Cryptic Cryptarithm

An entry in Fortnightly Topic Challenge #48: Unusual tag mix Solve these puzzles to reveal why I made them. Matriarch mostly prepared oats for American airline location? (8) AIRLINE + LOCATION = ? 51 ...
6
votes
2answers
286 views

Pandigital fraction sum that evaluates to 1

Fill in the nine X spots in the following equation using each of 1, 2, ..., 9 exactly once, so that the equation is satisfied. The XX in the denominator denotes concatenation of two digits. $$ \frac{X}...
4
votes
1answer
204 views

Solving Kordemsky's Prime Cryptarithm and proving uniqueness

This is a cryptarithm from Kordemsky's The Moscow Puzzles, problem 273 to be precise. Each digit is a single-digit prime ($2,3,5,$ or $7$). Find a solution and prove that it is unique. $$\begin{array}{...
7
votes
1answer
658 views

Long division cryptarithm - KLMN/HIJ = K

The problem statement: Solve the following long division problem. Each letter represents a unique digit (0-9) ...
2
votes
1answer
119 views

Does this alphametic have only one solution?

I could only get one answer for the following alphametic. Can you confirm? ETAS / (E * T * A * S) = SEAT - SATE All 4 lettes are separate digits from 1 to 9. ETAS, SEAT and SATE are 4 digit numbers ...
0
votes
4answers
253 views

Addition table with hidden digits

Similar to the previous puzzle, find the values behind the letters. ...
6
votes
2answers
348 views

Alphametic puzzle for Halloween

An alphametic puzzle for Halloween: OCT * 31 = TRICK + TREAT
1
vote
2answers
114 views

Sum with letters, find the values

In the following addition setup, each letter correspond to a unique digit. Find the different values of the letters. Requirement: r is not equal to 0. ...
0
votes
2answers
265 views

Coffee theorem puzzle [duplicate]

I am back yet with another puzzle, my last one was made this morning, and this one is a copied one from an app/website called Brilliant. So, this is especially for those who do not have Brilliant ...
1
vote
2answers
235 views

Cryptarithmetic: 1+1=0?

Transcription: ...
3
votes
2answers
518 views

A greedy cryptarithm

Find all solutions to EAT ATE + EATEN ------- YUMMY Where different letters represent different digits from 0 to 9. Problem by myself
10
votes
1answer
347 views

Old Bob is ill : Said Grandpa

“Darn good computer, this new one I just got. So you can have my old one”, said Grandpa to my sister. I was impressed, but a bit cynical. “What’s the catch?” Grandpa smiled. “Just guess the 4 letter ...
23
votes
1answer
977 views

Three part chess problem

Three separate puzzles: ...
5
votes
1answer
397 views

FORTY9 Cryptarithm

This puzzle is due to the amazing Martin Gardner and I found it here. Can you find which digit each letter represents to make the following sum work? Each letter is a single unique digit between 0 ...
-2
votes
2answers
167 views

What number does each color in the image represent?

This puzzle was part of a competition at my school, over two weeks ago. The school never disclosed the answer, so I'd like to check that I answered it correctly. What number does each color in the ...
4
votes
2answers
183 views

Solving an alphametic puzzle by eavesdropping

I took part in a meeting of puzzle maniacs. I overheard a conversation between two persons. A: Hey, solve this alphametic problem. LHS is a square of two-digit number and RHS is a four-digit number. ...
3
votes
1answer
182 views

Guess the missing digits [duplicate]

Can you guess the missing digits in the following multiplication? ??? x 3? = ???? Digits from 1 to 9 appear exactly once each. The goal is to solve it with as little calculation as possible.
16
votes
5answers
3k views

Four + Five = Nine

Obviously, FOUR + FIVE = NINE, but what if each letter is assigned a digit (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and two different letters can't be assigned the same digit? Fill in numbers for the ...
9
votes
1answer
163 views

Bilingual cryptarithm

This is a cryptarithm puzzle I found in a mathematical contest in 2004. The questions were available on the website of the of the AQJM (in french, Association Québécoise des jeux mathématiques) and we ...
1
vote
1answer
425 views

Math puzzle with logic programming

I had below question in one of my assignments for Login Programming for Artificial Intelligence topic. Solve the alphametic:     $ ABCDE $ $+$ $ CFGH$   --------...
3
votes
2answers
176 views

Greedy for Cash

Solve this Cryptarithm GIVE + MORE --------- MONEY Referenced from the Britannica Encyclopaedia No. 25 - "Number Prague"
3
votes
1answer
122 views

Alphametic puzzle, involving square and prime numbers [closed]

I have been trying puzzle solving recently and came across this problem. Any hints on how to do this? So far, I have found that N, R and F must be odd (as they are the last digit in a 5 digit prime ...
0
votes
3answers
230 views

Crypt Arithematic problem

Solve this Alphametic puzzle    T H I S + S I Z E ========= S H O R T
0
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1answer
123 views

Why two IA creates problems? [closed]

IA creates lots of debates about potential problems such as overtaking humans or destroying jobs. I'm not sure about AI but since 1985 Terminator, I know that two IA ("Intelligence Artificielle) ...
8
votes
2answers
228 views

Crossnumber puzzle

This is a numeric crossword: all the answers are positive numbers with no leading zeroes. Each clue is given as a sequence of mathematical operations on letters, each of which represents a distinct ...
2
votes
1answer
157 views

Mystic Island Math - Can you Figure it out?

On Mystic Island math is done via symbols. Distinct symbols represent distinct digits, varying from 0 to 9. From the picture below, figure out the corresponding digits. Please provide your reasoning....
9
votes
3answers
4k views

Too early in the morning to have SODA?

Each letter shown represent distinct digit...can vary from zero to nine. $COCA$, $COLA$, $SODA$ are three concatenated numbers. Figure these out from the following relation: $COCA + COLA = SODA$
-1
votes
1answer
143 views

SOLV for Narcissistic UVC

This puzzle highlights some cyclic power Relations. Please provide detailed reasoning of derivation of digits from various power relations given below: $Given$: $A$, $C$, $L$, $N$, $O$, $S$, $U$, $...
0
votes
2answers
105 views

Uvc with Lots of Magic... Enjoy the Show!

Puzzling Weekend! UVc is back again with Lots of Magic... Enjoy the Show! Given: LOTS is being multiplied by F to yield MAGIC. Digit 0 to 9 are all represented by ten different letters in this ...
7
votes
1answer
409 views

It is as easy as A B C, Figure out U V C from the given relationship

Given $ U, V, C $ are three distinct digits, figure them out from the following relation: $$ \overline{CCC} = \overline{UVUVUV} \div \left ( \overline{UV} \times \overline{UV} \right) $$
5
votes
2answers
711 views

Madam I m Adam..please don’t get mad..you will no longer be prime

Take away $ \overline{MAD} $ from $ \overline{MADMADAM} $ to make her prime. $ \overline{ADAM} $ is prime too if he does not get mad: $ \overline{MADADAM}. $ $ M, A, D $ are 3 distinct digits that ...
10
votes
3answers
478 views

No won won? Wone Won

Find four different digits $ W, O, N, E $ that satisfies the equation $$ \overline{NO} \times \overline{WON} \times \overline{WON} = \overline{WONEWON} $$
6
votes
1answer
267 views

It is as simple as ABC

Find three different digits $ A, B, C $ that satisfies the equation $ \overline{ABC} \times \overline{AA} \times \overline{AB} \times C = \...
6
votes
3answers
743 views

Find magical solution to magical equation

Solve this magical equation: $$ (M+A+G+I+C) \times (M+A+G+I+C) \times (M+A+G+I+C) = \overline{MAGIC} $$ Each letter represents a separate digit.
14
votes
4answers
2k views

Adding up numbers in Portuguese is strange

My friend from Portugal said that 2 + 2 is 8 in Portuguese. And he could prove it. I did not understand it at first. But then he showed me the following equation: ...
6
votes
2answers
351 views

Of course, *I* could solve this easily

Question: What do you think about music? Encoded below is part of one of my favorite songs. Rejoice, as the key to decrypt it is a common pattern. The type of thing you might see everyday. You should ...
7
votes
3answers
598 views

Three Visual Puzzles

I'm designing a puzzle game, and am trying to play-test some concepts. Can you solve these? 108153767833 = A + B + C. What are the components and why? Note for C: As a hint to correct an oversight, ...
7
votes
3answers
786 views

No spanish required

Each letter represents a digit, so what is Mucho and Poco (although who's to say?) ...
4
votes
2answers
226 views

$109088$ as sum of $3$ palindromes

One can write the number $109088$ as the sum of two palindromic numbers as follows: $$109088 = 99199 + 9889$$ Note that the numbers on the right are both palindromes (read the same left to right as ...
1
vote
2answers
801 views

K, L, M, K, L, M, ... what is the pattern? It is not what you first think

Everyone knows the J Family. It is the family where the names of the three sons and three daughters of Mr and Mrs Jameson each start with the letter J. Three Boys: Jordan; Jasper; and Jeremy. ...
11
votes
1answer
403 views

Endless investigation for ultimate truth

An alphametic puzzle containing 42. Don't panic although this is so big. Note that it contains the decimal point and thus several * must be 0. Here's an ascii version for easier editing: * ...
10
votes
2answers
2k views

What is his phone number?

Edit One day when you are watching your neighbor's dogs (one named Morse and the other named "nag a ram") the dog starts to have problems. Nag a ram will not stop crying/yelping and looks sad, so you ...
0
votes
3answers
757 views

How do I solve this odd puzzle?

I need help. Try to solve this puzzle. It's a blend of mathematics and words. The goal of word math problems is to assign each letter an integer value, 0-9. An example is below. Example: ...
0
votes
2answers
287 views

CITEMAHPLA Reverse Alphametic

Attempt at a Reverse Alphametic puzzle with a mathematically correct equation: 68053 + 2531 = 70584 Replace all the numbers with English letters (same number: same letter, so totally 9 separate ...
11
votes
1answer
1k views

What are these numbers?

A simple (I think) alphametic puzzle $\small{MADMEN = (M+A+D+M+E+N)^{((M+E+N) - (M+A+D))}}$ M,A,D,E,N are different (no repeats) positive integers between 0 and 9 and of course the 2 Ms are the ...
4
votes
7answers
378 views

Sum of three six digit numbers

This puzzle is a variation of a 3 digit addition puzzle I saw recently. A , B , and C are positive integers between 0 and 9. A,B and C are different integers Six digit numbers formed using A,B and ...