# Questions tagged [alphametic]

Alphametic puzzles involve equations where digits have been replaced with letters.

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### 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. ...
159 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 ...
203 views

### Cryptarithmetic: 1+1=0?

Transcription: ...
437 views

### A greedy cryptarithm

Find all solutions to $$\begin{array}& & & &E&A&T\\& & &A&T&E\\+&E&A&T&E&N\\\hline&Y&U&M&M&Y\end{array}$$ Where ...
243 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 ...
934 views

### Three part chess problem

Three separate puzzles: ...
356 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 ...
144 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 ...
169 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. ...
175 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.
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 ...
149 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 ...
383 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:     $ABCDE$ $+$ $CFGH$   --------...
173 views

### Greedy for Cash

Solve this Cryptarithm GIVE + MORE --------- MONEY Referenced from the Britannica Encyclopaedia No. 25 - "Number Prague"
113 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 ...
213 views

### Crypt Arithematic problem

Solve this Alphametic puzzle    T H I S + S I Z E ========= S H O R T
119 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) ...
204 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 ...
149 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....
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: $COCA + COLA = SODA$
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### 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.
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: ...
342 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 ...
584 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, ...
779 views

### No spanish required

Each letter represents a digit, so what is Mucho and Poco (although who's to say?) ...
192 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 ...
607 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. ...
389 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: * ...
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 ...
735 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: ...
271 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 ...
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 ...
367 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 ...
142 views

### How many answers are there to this alphametic?

If you take a problem of the form: abc +def ---- ghij where each letter must be replaced by a different digit (that is, all digits, 0-9 must be used once), how ...
413 views

### Decipher this puzzle

This is my riddle for you, to solve it you need to decipher the letters to digits: j m b k + n h s m --------- n h b m t the following rules must apply: ...
345 views

### 1 crossword and 2 connected alphametic (more clues)

Rules : Solve the Crossword. The words can be written backward (example zebra -> arbez) After finishing the crossword, solve the alphametics. The crossword is only uses 10 letters. Each letter ...
214 views

### Archaeological alphametic

Enigmarchaeologists uncovered an ancient Roman precursor to our familiar, and comparatively dignified,   SEND + MORE = MONEY  alphametic.   ...
212 views

### Scottish Letter Equation

The following puzzle is from a Scottish mathematical competition and has been posed at the Jordanhill school in Glasgow: A shop sells letter signs, and the price of every letter is an integer number ...
1k views

### One year celebration

I've got notified a few days ago from PSE that my account on this website is 1 year old. So I thought about celebrating it (or commemorating it, because you all made me addicted to this) with a puzzle ...
625 views

### Long Division Logic Problem

I know some of you enjoy some good math logic problems (Myself included) here is one I had fun with that took me a bit of time to solve. The A in these numbers is a number 0-9, it is the same number ...
844 views

### Factoring puzzle

I have an amazing puzzle that should be a little difficult even for you awesome puzzlers. $(ab)^c = def × ghij$ where each letter stands for a number from 0 to 9 (inclusive). Each digit must be ...
352 views

### Alphametic puzzle for year 2017

In east Asia 2017 is the year of a rooster. $$ABCD=\left(A \times CA^A + \frac{C}{D} \right) \times D$$
Replace letters with numbers 1 to 9, so the 3 operations below are equals. Each letter represents one unique number. $$\frac{ab}{c} = de \times f = gh - i$$