Tool/solver to resolve cryptarithms, a numeric puzzle which consists in a mathematical calculation in which letters have been replaced by digits to find.

Cryptarithm Solver - dCode

Tag(s) : Number Games, Arithmetics

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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:

⮞ Go to: Missing Numbers Calculator

**Alphametics** (also called **cryptarithm**) solving involves deduction and use of calculation tricks.

Method 1 (automatic): use the above solver, it tries all possible digits for all letters.

Some **Alphametics** comes under the form:

AB

×C

--------

DE

+FG

---------

HI

Please rewrite it in two parts AB*C=DE+FG && DE+FG=HI for the solver

Method 2 (manual): deduction, logic and principles of mathematical calculations according to a few rules:

- Each letter can be associated to only one digit (appropriate numeral from 0 to 9). 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 usually do not start with a zero 0

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

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.

A **cryptarithm** is a number puzzle representing an arithmetic 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. The term **alphametics** is also used when the letters form a real word.

__Example:__ DONALD + GERALD = ROBERT

BASE + BALL = GAMES

LLP + LINEAR + LOGIC = PROLOG

LOGIC + LOGIC = PROLOG

CROSS + ROADS = DANGER

SATURN + URANUS = PLANETS

ABC + ABC + ABC = BBB

AB + BC + CA = ABC

XX + YY + ZZ = XYZ

XXXX + YYYY + ZZZZ = YXXXZ

XXXX + YYYY + ZZZZ = XYYYZ

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

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

Please, check our dCode Discord community for help requests!

NB: for encrypted messages, test our automatic cipher identifier!

cryptarithm,cryptarithmetic,alphametic,equation,calculation,letter,digit,addition,multiplication,plus,minus,equal,puzzle,send,more,money,substitution

Source : https://www.dcode.fr/cryptarithm-solver

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