Sudoku X: free diagonal sudoku

Sudoku X: sudoku with diagonals

Sudoku X is classic 9×9 sudoku with one more rule. Every row, column and 3×3 box must hold the digits 1 to 9, as usual, and so must the two long diagonals that run from corner to corner. That is why it is also called diagonal sudoku. On the board the diagonal cells are shaded, so the extra lines are easy to follow.

The puzzles here are generated fresh each time at a medium level. Each one has a single solution you can reach by logic, without guessing.

How the diagonals change the game

In normal sudoku every cell belongs to three groups: its row, its column and its box. In sudoku X, the 17 cells on the diagonals belong to four, and the centre cell belongs to five, since it sits on both diagonals. More groups means more ways to rule digits out, so diagonal cells tend to resolve earlier than the cells around them.

Because the extra rule gives so much information, a sudoku X usually starts with fewer clues than a normal puzzle of the same difficulty. The first few moves can feel bare, until you start using the diagonals.

Extra techniques for sudoku X

The usual tools all still apply: singles, pairs, pointing pairs and box-line reduction. The diagonals add a few of their own.

1. Diagonal singles. Scan each diagonal like a row. If a digit has only one possible cell left on a diagonal, it goes there, even if that cell has other candidates.
2. Diagonal pointing. If, inside a corner box, a digit’s candidates all sit on the diagonal, that digit must be on the diagonal in that box. Remove it from the other cells of the same diagonal.
3. The reverse. If, on a diagonal, a digit can only fit in cells that lie inside one box, remove it from the rest of that box.
4. Crossing cells. The centre cell is shared by both diagonals. A digit placed there is removed from all 16 other diagonal cells at once.
5. Pairs on a diagonal. Two diagonal cells with the same two candidates form a naked pair, just as in a row. Remove those two digits from the other seven cells of that diagonal.

A good routine

Begin with the centre box and the centre cell, where the most rules meet. Then sweep both diagonals for missing digits before doing ordinary row and column scanning. When you add pencil marks, always include the diagonal in your check: forgetting it is the most common mistake in sudoku X.

Where it fits

If medium sudoku feels comfortable, sudoku X is a good next twist, because it rewards the same skills with a new rule. For a different variant, jigsaw sudoku swaps the square boxes for irregular shapes, and killer sudoku adds cage sums.

How to play here

Tap a cell and type a digit, or use the number pad on a phone. For pencil marks, right-click a cell on a computer, or switch on Mark mode on a phone before entering digits. New puzzle deals a fresh diagonal grid whenever you want one.

How to play Sudoku X

1. Fill every empty cell with a digit from 1 to 9.
2. Each row, each column and each 3×3 box must contain every digit exactly once.
3. The two long diagonals, corner to corner, must also contain every digit exactly once.
4. The diagonal cells are shaded on the board so you can see them at a glance.

Sudoku X tips

Start with the centre cell

The centre cell sits on both diagonals, in the middle row, the middle column and the middle box. Five constraints meet there, so it is often the first cell to fall.

Treat each diagonal as a tenth line

Scan the diagonals the way you scan rows. A diagonal with seven digits has two gaps, and the missing digits often settle both cells.

Watch the corner boxes

Each corner box has three diagonal cells, and the centre box has five. A digit placed on a diagonal in one of them clears it from all the other cells of that diagonal.

Frequently asked questions