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Cryptarithm Solver

Tool/solver to resolve cryptarithms. A Cryptarithm is a numeric puzzle which consists in a mathematical equation in which letters are substituted by digits to recover.

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Cryptarithm Solver -

Tag(s) : Number Games, Arithmetics

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# Cryptarithm Solver

## Other Calculation with Letters?

To get more results associating several numbers with the same letter or several letters with the same number, replace the letters by a '?' (question mark) and use the fill-the-blank solver:

Tool/solver to resolve cryptarithms. A Cryptarithm is a numeric puzzle which consists in a mathematical equation in which letters are substituted by digits to recover.

### How to solve cryptarithms?

Alphametics (also called cryptarithm) solving involves deduction and use of calculation tricks. Usually, remember the rules:

- Each letter can be associated to only one digit and reciprocally each digit can be associated to only one letter

If your calculation do not follow this rule, then use the missing numbers solver.

- Numbers do not have leading zeros

The resolution then goes through the search for particular cases:

- addition/subtraction with 0 or 9

Example: ??A+??A=??A then A is 0

Example: ?A?+?A?=?A? then A is 0 or 9, same for ?A?+?B?=?B? or ??A+??B=??B

- first digits and last digits

Example: ???+???=A??? then A is 1 because it is impossible that the sum of 2 numbers less than 1000 is superior to 1999.

- multiplications by 0, 1 or 5 and squaring

Example: A*A=?B then A is not 0, 1 or 5

- multiplications of numbers with n and m digits that create numbers with n + m digits

- divisions by 1 ou 5

Do not hesitate to make attempts when there are few possibilities

Some Alphametics comes under the form:
AB
×C
--------
DE
+FG
---------
HI
to rewrite in two parts AB*C=DE+FG && DE+FG=HI for the solver

### How does the cryptarithm solver works?

dCode cryptarithm solver handles classical mathematical operators like additions + (plus), subtractions - (minus), multiplications * (times) and divisions /. It also handles logical conditions like && = ET, || = OU and also comparators superior and inferior > and <.

The solver takes for unknown between 1 and 10 distinct letters.

Example: A+A=B && B*C=AB is solved with 2+2=4 && 4*6=24

Example: DCODE+CODING=SOLVED => 92095+209764==301859.

This alphametic solver uses brute-force, ie. it tries all combinations of digits and displays the possible ones.

### What is the definition of cryptarithmetics?

A cryptarithm is a number puzzle representing an arithmetical equation (with an equal = sign) in which some or all of its digits has been replaced by a substitution of letters or symbols. The goal is to find the digits represented by the letters. Alphametics is also used when the letters forms a real word.

### Why SEND+MORE=MONEY?

It is the most known example of cryptarithm (or alphametic), published in 1924 in Strand Magazine, by Henry Dudeney : S E N D + M O R E = M O N E Y . Solution is O=0, M=1, Y=2, E=5, N=6, D=7, R=8, and S=9.

## Source code

dCode retains ownership of the online 'Cryptarithm Solver' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Cryptarithm Solver download for offline use on PC, tablet, iPhone or Android !

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