Cryptarithm Solver

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.

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

— 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

— first digits and last digits

— multiplications by 0, 1 or 5 and squaring

— 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.

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is a number puzzle representing an arithmetic equation (with an equal = sign) in which some or all of its digits has been replaced by a substitution of letters or symbols.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

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.