Cryptarithm Solver — Step-by-Step Alphametic Solutions
Enter a cryptarithmetic puzzle with addition, subtraction, or multiplication. The solver finds every answer and, when there is exactly one, explains how to reach it.
How to enter a puzzle
Choose addition, subtraction, or multiplication, then type one word on each line and the result below the rule. Each letter stands for one digit, different letters stand for different digits, and a number with more than one digit cannot start with 0.
Addition can have up to ten words, as in STORK + KOI + BOAS + TROUT + TOADS + RATS = BIRDS. Subtraction and multiplication take exactly two words. A puzzle can use at most ten different letters.
How the reasoning works
For addition, the solver reads the puzzle column by column from the right: the digits in a column plus the incoming carry equal the result digit plus ten times the outgoing carry. A subtraction A − B = C is checked as the addition B + C = A.
For multiplication, the last digits of the product depend only on the last digits of the two factors, and the leading digits limit how large the product can be.
When no column gives a direct answer, the solver assumes one value and shows the contradiction it causes. If that is still not enough, it checks each remaining case in turn.
Several answers or none
If more than one assignment works, the solver lists the answers instead of a single chain of deductions. If none works, it shows where the contradiction appears.
Puzzles are solved in your browser. What you type is not sent to our server.