🔢 How to play X-Sums Sudoku

By Miguel Arechaga

X-Sums Sudoku is a clever sum-based variant, common in international competitions. The clues sit outside the board, but with a twist: they don't add up the whole line, only its first few cells, and how many cells get summed is decided by the first number in the line. Here are the rules and a few tips.

What is X-Sums Sudoku?

It's a standard 9x9 sudoku where, next to some rows and columns, a number appears. That number is the sum of the first N cells of the line, counting from the edge where the clue sits. And the key part: N is the value of the first cell (the one closest to the clue). The "X" in the name stands for that "unknown number" of cells being summed.

Rules and how to play step by step

1. The sudoku rules apply: 1 to 9 without repeats in each row, column and 3x3 box.
2. The outer clue is the sum of the first N cells of that line.
3. N = the number in the first cell. If the first cell is a 4, you sum the first 4 cells.
4. You start with some clue cells and fill in the rest with logic. Every puzzle has a unique solution.

Tips to solve X-Sums Sudoku

• Clue equal to a single digit: if the clue is 1, the first cell is a 1 (sum of 1 cell). If it's 3 and only fits with the first cell alone, that fixes it too.
• Clue of 45: means it sums the whole row (1+2+...+9 = 45), so the first cell is a 9.
• Bound N: a small sum implies few cells (and so a low first cell); a large sum implies many cells.
• Combine deducing the first number with the classic elimination techniques of sudoku.

How it differs from regular sudoku

Compared to classic sudoku, X-Sums ties the clue to both the position and the value of the first cell, producing very elegant deductions. It's a cousin of Sandwich Sudoku and Little Killer Sudoku. If you enjoy variants with outer sums, you'll love it.