Cryptarithm Solver

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

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is a number puzzle representing an arithmetical equation (with an equal = sign) in which some or all of its digits has been replaced by a substitution of letters or symbols.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.

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.