How to play Letter Sums

Replace each letter with a digit — different letters, different digits, no leading zeros — so that every sum is correct. Also known as Cryptarithm, Alphametic, Code sums, Letter arithmetic.

▶ Play Letter Sums ⊞ Open the solver

The rules

Each letter stands for one digit from 0 to 9.
The same letter is always the same digit, and different letters are different digits.
No number starts with 0.
In code sums, all the sums use the same code; the letters for 0 to 9, in order, spell the hidden word.

Playing Letter Sums on Puzzle Solvers

Choose Code sums (find a hidden word) or Word sums (classic letter additions), and a difficulty, then press New Puzzle.
Use the code board: tap a square to match a letter to a digit (⭕), or switch to Rule out (✕) to cross options off. You can also click a letter and type its digit.
Your digits appear under the letters, and each sum gets a ✓ when it works.
Hint explains the next deduction column by column — carries, no leading zeros, and digits that can’t fit.

Open the Letter Sums game →

Using the Letter Sums solver

Type one or more sums using + − × and = (up to 10 different letters).
Press Solve and step through: leading letters, carries, what each column allows, and what-ifs, until every letter has its digit.

Open the solver →

A worked example

SEND + MORE = MONEY. The answer has five digits and the numbers four, so M = 1.

Then S + M (+ carry) makes a two-digit number starting with 1 — S must be 9 and O = 0. Working along the columns gives O = 0, E = 5, N = 6, D = 7, R = 8, Y = 2: 9567 + 1085 = 10652.

Strategies

The extra digit. If two numbers add up to an answer with one more digit, that first digit is a carry — it must be 1.
Units first. The last column has no carry coming in: D + E must end in Y.
Carries. Each column’s total is the letters plus any carry from the right; a carry is never more than 1 when adding two numbers.
Same letter, both sides. In a column like A + B = A (with a carry), B must be 9 or 0.
Zero and nine. A column where X + Y = X with no carry means Y = 0; with a carry in and out, Y = 9.

Common mistakes

Giving two letters the same digit.
Forgetting the carry from the column to the right.
Letting a number start with 0.

Where it comes from

Letter sums go back over a century. The most famous, SEND + MORE = MONEY, was published by the English puzzle writer Henry Dudeney in The Strand Magazine in 1924.

Frequently asked questions

How do code sums work?

All the sums share one code. When you’ve matched every letter to a digit, read the letters for 0, 1, 2 … 9 — they spell a ten-letter word.

Can I use subtraction or multiplication?

Yes — code sums at higher levels use − and ×, and the solver accepts them too.

Is there always one answer?

Yes — every puzzle here is checked to have exactly one solution.

How do I solve one I found elsewhere?

Open the Letter Sums Solver, type the sums and press Solve.

Keep going

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