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Cryptarithm Solver

Tool to solve 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 Game, Arithmetics

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# Cryptarithm Solver

## Cryptarithm/Alphametic Solving

Tool to solve 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 a Cryptarithm?

Alphametics 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, idem for ??A+??B=??B

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

- multiplication by 0, 1 or 5

- divisions by 1 ou 5

Do nothesitate to make attempts when there are few possibilities

### How does the cryptarithm solver works?

dCode cryptarithm solver handles classical mathematical operators like additions +, subtractions -, multiplications * 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 a brute-force method, this means that it tries all combinations and displays the possible ones.

### What is the definition of cryptarithmetics?

A cryptarithm is a number puzzle representing an arithmetical equation in which some or all of its digits has been replaced by letters or symbols. The goal is to find to which letter is corresponds. Alphametics is also used when the letters forms a real word.

### Why SEND+MORE=MONEY?

It is the most known example, 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.