Does every puzzle have exactly one answer?

Yes, and it is checked rather than assumed. The solver looks for a second solution and the puzzle is discarded if it finds one.

Why does no number start with zero?

Because a number written with a leading zero is not how we write numbers, and allowing it gives most of these puzzles extra answers that are not interesting.

Where do the word sets come from?

They are a hand-picked list of classic and readable sums. Generating phrases at random produces valid arithmetic that reads like nonsense, which is a worse puzzle.

Cryptarithm Generator

A cryptarithm is a sum written in letters. Each letter stands for a different digit, no number may begin with a zero, and there is exactly one assignment that makes the arithmetic work. The classic is SEND + MORE = MONEY, which has precisely one answer out of the millions available. Every puzzle offered here is solved before it is shown, so you are never handed one with two answers or none.

Seed (optional)

A word brings the same puzzle back, so a class can all work on it.

Your puzzle will appear here.

What this generator does

Offers a sum written in letters and confirms, before showing it, that exactly one digit assignment satisfies it. Puzzles with no solution or more than one are discarded rather than presented, which matters because a cryptarithm with two answers is not a puzzle — it is a trick.

How to use this tool

Press make a puzzle to get a sum written in letters.
Work out which digit each letter stands for. No leading zeros.
Reveal the answer to check your assignment.
Use a seed to give several people the same puzzle.

Understanding the controls

Seed: Any word reproduces the same puzzle. Without one you get a different draw each time from the browser's cryptographic generator.
Show the answer: Reveals the digit for each letter and writes the sum out in numbers, so you can see the arithmetic rather than just be told you were right.

Common use cases

A logic and arithmetic starter that needs no equipment
Showing how much constraint a small number of rules can carry
A puzzle for someone who likes Sudoku but wants arithmetic in it
Demonstrating carrying in addition from the other direction
A shared puzzle for a group, generated from one seed

How this generator works

The puzzle is solved column by column from the right, carrying as it goes, rather than by trying every letter-to-digit assignment. That distinction is what makes it instant: enumerating assignments for a nine-letter puzzle means 3.6 million possibilities and measured about a second and a half, while checking each column's arithmetic as soon as its letters are known prunes nearly all of that and finishes in about a millisecond. The search stops as soon as it finds a second solution, because more than one is all the information needed to reject a candidate.

Randomness and fairness

Which puzzle you are given is random; its having one answer is not. Without a seed the draw uses the browser's cryptographically secure generator; with a seed a small deterministic one, which is reproducible and therefore explicitly not cryptographically secure.

For how randomness is produced across the whole site, see how Generate Random works.

Assumptions this tool makes

Each distinct letter maps to a distinct digit from 0 to 9.
No multi-digit number in the puzzle begins with a zero.

Limitations and good to know

The word sets are a hand-picked list rather than generated, because sums that read as real phrases cannot be produced at random.
Only addition is offered. Subtraction and multiplication cryptarithms exist but read very differently and are not covered here.
There is no difficulty grading, and no hint system — it confirms the answer rather than teaching the deduction.
Nothing is saved between visits, so seed anything you want to keep.

Common mistakes

Letting two letters share a digit: Every letter is a different digit. That is the constraint doing most of the work, and dropping it usually creates several answers.
Allowing a leading zero: No number in the sum may start with zero. Without this rule most of these puzzles gain extra trivial answers.
Starting from the left: The rightmost column has no carry coming into it, so it is the only one you can reason about without assumptions. Work right to left, as the solver does.

Practical tips

If the result is one digit longer than the addends, its leading letter must be 1 — a sum of two numbers can only carry one.
Look for a letter that appears in the same column as itself; those columns pin down carries quickly.
Work in pencil and track which digits are still unused. The uniqueness constraint is what closes the puzzle out.

Privacy and your data

Puzzles are generated in your browser. Nothing you type or copy is sent anywhere or stored between visits.

Frequently asked questions

Does every puzzle have exactly one answer?: Yes, and it is checked rather than assumed. The solver looks for a second solution and the puzzle is discarded if it finds one.
Why does no number start with zero?: Because a number written with a leading zero is not how we write numbers, and allowing it gives most of these puzzles extra answers that are not interesting.
Where do the word sets come from?: They are a hand-picked list of classic and readable sums. Generating phrases at random produces valid arithmetic that reads like nonsense, which is a worse puzzle.