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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BROWN + YELLOW = PURPLE [closed]

This is a Cryptoarithmatic, where each letter denotes a single digit number. Find values of all the letters. BROWN + YELLOW = PURPLE Please show your method for solving this question.
Anuraj's user avatar
  • 69
6 votes
5 answers
3k views

Math is Awesome

I have a shirt. It says that $AWE+SOME=MATH.$ A, W, E, S, O, T, M, and H are not necessarily distinct positive integers from $0$ to $9$. The goal is to find the maximum possible value of $MATH.$ If ...
Ronchen Luo's user avatar
9 votes
1 answer
359 views

Cryptic Division 8: Business as Usual

This is a word division puzzle which uses cryptic clues. If you're unfamiliar with either or both of those, you can click the associated link. In order to solve the alphametic, you'll first need to ...
juicifer's user avatar
  • 10.4k
8 votes
2 answers
285 views

Cryptic Division 7: Nothing Under the Tree

This is a word division puzzle which uses cryptic clues. If you're unfamiliar with either or both of those, you can click the associated link. In order to solve the alphametic, you'll first need to ...
juicifer's user avatar
  • 10.4k
7 votes
1 answer
143 views

Cryptic Division 6: It's All Gravy

This is a word division puzzle which uses cryptic clues. If you're unfamiliar with either or both of those, you can click the associated link. In order to solve the alphametic, you'll first need to ...
juicifer's user avatar
  • 10.4k
8 votes
1 answer
367 views

Cryptic Division 5: Devil Magic

This is a word division puzzle which uses cryp- actually, this one uses printer's devilry. If you're unfamiliar with either or both of those, you can click the associated link. In order to solve the ...
juicifer's user avatar
  • 10.4k
10 votes
2 answers
491 views

Shiny cryptarithm

Here's a little puzzle I made today: $$\sqrt{\text{ILLUMINATE}^{\mathstrut}} = \text{LIGHT}$$ Most usual rules of alphametic puzzles apply here: the same letter always represents the same digit, and ...
Greg Martin's user avatar
  • 1,160
11 votes
1 answer
727 views

Cryptic Division 4: Oops! All Math!

This is a word division puzzle which uses cryptic clues. If you're unfamiliar with either or both of those, you can click the associated link. In order to solve the alphametic, you'll first need to ...
juicifer's user avatar
  • 10.4k
17 votes
1 answer
453 views

Cryptic Division 3: Stuck Together

This is a word division puzzle which uses cryptic clues. If you're unfamiliar with either or both of those, you can click the associated link. In order to solve the alphametic, you'll first need to ...
juicifer's user avatar
  • 10.4k
10 votes
2 answers
180 views

Cryptic Division 2: Staying on Brand

This is a word division puzzle which uses cryptic clues. If you're unfamiliar with either or both of those, you can click the associated link. In order to solve the alphametic, you'll first need to ...
juicifer's user avatar
  • 10.4k
11 votes
1 answer
375 views

Solidarity with the Moderation Team (A Cryptic Division Puzzle)

Alternative title: Cryptic Division 1: Never Give Up This is a word division puzzle which uses cryptic clues. If you're unfamiliar with either or both of those, you can click the associated link. In ...
juicifer's user avatar
  • 10.4k
4 votes
8 answers
2k views

The Era Of The Ear

Given this information, \begin{matrix} & E & R & A \\ + & E & A & R \\ \hline & A & R & E \\ \end{matrix} What is the sum of $A$, $R$, and $E$ and if you can ...
RonnieChen's user avatar
12 votes
1 answer
996 views

Laughing At The Wrong Time

Uh... Every letter corresponds to a different digit and 0 cannot be a leading digit. Find $HA+UH$ if $$\begin{array}{cccc} & H & A \\ + & H & A \\ + & H & A \\ + & H &...
Ronchen Luo's user avatar
4 votes
1 answer
439 views

Need help solving a multiplication puzzle

The puzzle goes as follows: Each letter corresponds to a number, what is the result of the multiplication? RQQ × P ___ QST I'm not sure where to start with this puzzle. I know that each letter ...
cricket900's user avatar
5 votes
1 answer
174 views

An alphametic division of all different digits

Here is a division process: ABCD / PQ = XYZ with remainder R. The ten letters A,B,C,D,P,Q,X,Y,Z,R are all different digits.
P.-S. Park's user avatar
  • 4,199
3 votes
1 answer
358 views

How to find the value that makes this addition equation work without using a computer?

The following image represents the addition of 2 five-digit numbers, where 10 different letters represent 10 different numbers (0~9). What does PUZZLE equal? (There are two possibilities and a ...
Pumbaa's user avatar
  • 938
1 vote
2 answers
233 views

An alphametic puzzle about Charles Darwin

Charles Darwin was born on February 12, 1809. https://en.wikipedia.org/wiki/Charles_Darwin
P.-S. Park's user avatar
  • 4,199
1 vote
1 answer
90 views

An alphametic puzzle about Thomas Edison

Thomas Alva Edison was born on February 11, 1847. https://en.wikipedia.org/wiki/Thomas_Edison
P.-S. Park's user avatar
  • 4,199
3 votes
1 answer
144 views

An alphametic puzzle about Jules Verne

Jules Verne was born on February 8,1828. https://en.wikipedia.org/wiki/Jules_Verne
P.-S. Park's user avatar
  • 4,199
2 votes
1 answer
125 views

In honor of Franz Schubert’s birthday, January 31

Franz Peter Schubert was born on January 31, 1797. Here is a skeletal division. Each music note denotes an odd or even digit. https://en.wikipedia.org/wiki/Franz_Schubert
P.-S. Park's user avatar
  • 4,199
5 votes
2 answers
226 views

In honor of Olof Palme’s birthday, January 30

Olof Palme, the prime minister of Sweden, was born on January 30, 1927. https://en.wikipedia.org/wiki/Olof_Palme Each Swedish flag can be assigned arbitrary digit.
P.-S. Park's user avatar
  • 4,199
3 votes
2 answers
222 views

In honor of Anton Chekhov’s birthday, January 29

Anton Pavlovich Chekhov, the Russian playwriter and novelist was born on January 29, 1860. https://en.wikipedia.org/wiki/Anton_Chekhov
P.-S. Park's user avatar
  • 4,199
8 votes
1 answer
583 views

In honor of Lewis Carroll’s birthday, January 27

Charles Lutwidge Dogdson, a.k.a. Lewis Carroll, is famous for his “ Alice's Adventures in Wonderland.” He was born on January 27, 1832.
P.-S. Park's user avatar
  • 4,199
7 votes
1 answer
324 views

In honor of David Hilbert's birthday, January 23

Here is a skeletal division to celebrate David Hilbert's birthday.
P.-S. Park's user avatar
  • 4,199
12 votes
6 answers
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. ...
DrD's user avatar
  • 39.2k
1 vote
0 answers
290 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 ...
Developer's user avatar
16 votes
2 answers
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.
Oshawott's user avatar
  • 271
4 votes
1 answer
306 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: ...
trolley813's user avatar
  • 11.3k
10 votes
1 answer
465 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 ...
samm82's user avatar
  • 7,243
6 votes
2 answers
306 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}...
Bubbler's user avatar
  • 12.2k
5 votes
1 answer
298 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}{...
Favst's user avatar
  • 153
7 votes
1 answer
1k views

Long division cryptarithm - KLMN/HIJ = K

The problem statement: Solve the following long division problem. Each letter represents a unique digit (0-9) ...
rohit's user avatar
  • 71
2 votes
1 answer
128 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 ...
DrD's user avatar
  • 39.2k
0 votes
3 answers
269 views

Addition table with hidden digits

Similar to the previous puzzle, find the values behind the letters. ...
Per Alexandersson's user avatar
6 votes
2 answers
373 views

Alphametic puzzle for Halloween

An alphametic puzzle for Halloween: OCT * 31 = TRICK + TREAT
P.-S. Park's user avatar
  • 4,199
1 vote
2 answers
146 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. ...
Per Alexandersson's user avatar
0 votes
2 answers
322 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 ...
user avatar
1 vote
2 answers
251 views

Cryptarithmetic: 1+1=0?

Transcription: ...
Shivansh Sharma's user avatar
3 votes
2 answers
542 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
Culver Kwan's user avatar
  • 5,570
10 votes
1 answer
362 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 ...
DrD's user avatar
  • 39.2k
23 votes
1 answer
1k views

Three part chess problem

Three separate puzzles: ...
Laska's user avatar
  • 1,869
5 votes
1 answer
603 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 ...
Dmitry Kamenetsky's user avatar
-2 votes
2 answers
244 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 ...
MissNature's user avatar
4 votes
2 answers
212 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. ...
P.-S. Park's user avatar
  • 4,199
3 votes
1 answer
187 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.
Jacques Gaudin's user avatar
16 votes
5 answers
4k 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 ...
CG.'s user avatar
  • 2,590
10 votes
1 answer
199 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 ...
Alain Remillard's user avatar
1 vote
1 answer
477 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$   --------...
Radiant's user avatar
  • 145
3 votes
2 answers
184 views

Greedy for Cash

Solve this Cryptarithm GIVE + MORE --------- MONEY Referenced from the Britannica Encyclopaedia No. 25 - "Number Prague"
Quark-epoch's user avatar
  • 1,697
3 votes
1 answer
127 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 ...
Jamminermit's user avatar