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Cryptarithm Solver

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to resolve cryptarithms, a numeric puzzle which consists in a mathematical calculation in which letters have been replaced by digits to find.

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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:

### How to solve cryptarithms?

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.

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

### How does the cryptarithm solver work?

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 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
SATURN + URANUS = PLANETS
ABC + ABC + ABC = BBB
AB + BC + CA = ABC
XX + YY + ZZ = XYZ
XXXX + YYYY + ZZZZ = YXXXZ
XXXX + YYYY + ZZZZ = XYYYZ

### Why SEND+MORE=MONEY?

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.

## Source code

dCode retains ownership of the online "Cryptarithm Solver" source code. Except explicit open source licence (indicated CC / Creative Commons / free), the "Cryptarithm Solver" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Cryptarithm Solver" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, copy-paste, or API access for "Cryptarithm Solver" are not public, same for offline use on PC, tablet, iPhone or Android ! Remainder : dCode is free to use.

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