What Is Cross Sums? The Number Puzzle With Two Names

You've probably seen this puzzle before, maybe under a different name. Cross Sums looks like a crossword that swapped its words for numbers: a grid of black and white squares, with little totals tucked into the black cells instead of clues like "5 Across: a French river." If you've heard of Kakuro, here's the twist — Cross Sums and Kakuro are the exact same puzzle. They're just two names for one of the most satisfying number games ever invented. This guide explains what a cross sums puzzle is, how it works, and how it ended up with a double identity. Then you can play it for yourself.

The short answer

Cross Sums is a number-placement puzzle played on a crossword-style grid, where you fill runs of white cells with the digits 1 to 9 so that each run adds up to a given total — without repeating a digit inside that run. "Cross Sums" is the original English name; "Kakuro" is the name it picked up in Japan, and the one most of the world uses today. Same grid, same rules, two labels.

What a cross sums grid looks like

Picture a small crossword. Some cells are black, some are white. In a word crossword, you'd fill the white cells with letters. In Cross Sums, you fill them with single digits, 1 through 9.

The clues live inside the black cells, and they're numbers, not word definitions. A black cell is split by a diagonal line:

• The number in the upper-right triangle is the target sum for the run of white cells stretching to its right (the "across" entry).
• The number in the lower-left triangle is the target sum for the run of white cells running down beneath it (the "down" entry).

So if a black cell shows a 6 in its upper-right corner and there are three white cells to its right, those three cells must contain three different digits that add up to 6 — which, as it happens, can only be 1, 2 and 3.

The two simple rules

For all its clever appearance, Cross Sums runs on just two rules:

1. Each run of white cells must add up to its target sum. A "run" (also called an entry) is an unbroken line of white cells, going across or down, bounded by black cells or the grid edge.
2. No digit may repeat within a single run. You can't make a sum of 4 in a two-cell entry with 2 + 2, because that repeats the 2 — it has to be 1 + 3.

That's genuinely all there is to the rules. Everything else is logic. (For a full visual walkthrough with worked examples, see how to play Kakuro.)

Why the same puzzle has two names

The double name is a small piece of puzzle history. The game was first published in the United States in the 1960s under the name "Cross Sums." It was a clever, math-flavoured alternative to the crossword, and it built a quiet following in puzzle magazines.

Then it travelled to Japan, where the famous puzzle publisher Nikoli — the same company that later launched the global Sudoku craze — gave it a Japanese name: "Kasan Kurosu," meaning "addition cross." Over time that got shortened to the snappier "Kakuro," and when the puzzle spread worldwide in the 2000s, the Japanese name travelled with it. Today "Kakuro" is the dominant name globally, while "Cross Sums" lingers in older publications and among solvers who met it first. You can read the full history of Kakuro for the complete journey.

So if you're hunting for "cross sums puzzles" online and keep landing on pages about "Kakuro," you haven't taken a wrong turn — you've found exactly the right puzzle.

Why people love it

Cross Sums hits a sweet spot that pure-logic puzzles like Sudoku don't quite reach. Because the numbers actually have to add up, every move involves a little burst of mental arithmetic, and there's a particular pleasure in spotting that a run "can only be" one combination of digits. It's a crossword's structure with a math puzzle's brain, and it's completely solvable by logic — no guessing, ever, in a well-made grid.

If you already enjoy Sudoku, Cross Sums is the obvious next step, adding a satisfying arithmetic layer to the elimination logic you already know. Curious how the two stack up? Our Kakuro vs Sudoku comparison breaks it down.

Now that you know Cross Sums and Kakuro are one and the same, there's only one thing left to do: try a puzzle. Play Cross Sums now, or brush up on the rules first.

Frequently asked questions

What is a cross sums puzzle?

A cross sums puzzle is a number game played on a crossword-style grid. You fill runs of white cells with the digits 1 to 9 so that each run adds up to a target sum shown in the adjoining black clue cell, and no digit repeats within a single run. It is solved entirely through logic and arithmetic, with no guessing required.

Is cross sums the same as Kakuro?

Yes, cross sums and Kakuro are the same puzzle with the same rules. "Cross Sums" is the original English name from the 1960s, while "Kakuro" is the name given by the Japanese publisher Nikoli (short for "Kasan Kurosu," meaning "addition cross"). Kakuro is now the more common name worldwide.

How do you solve a cross sums puzzle?

You work out which combinations of different digits can produce each target sum, then use the points where across and down runs cross to eliminate possibilities. Short runs with extreme sums are the best starting points — for example, a two-cell run summing to 3 can only be 1 + 2 — and these forced combinations unlock the rest of the grid.

Why is it called cross sums?

It's called cross sums because the puzzle combines a crossword-style grid (the "cross") with addition (the "sums"). Runs of cells cross each other just like words in a crossword, but instead of spelling words, each run must add up to a specified total.