Sudoku X Rules: How to Play (With a Printable Example)

The Sudoku X rules add a single line to classic Sudoku: the two long diagonals must also contain the digits 1 to 9 once each. If you know how to play Sudoku, you can play Sudoku X after reading this page. If you do not, the rules are explained from the start, with a real grid whose diagonals you can check by hand.

The rules

1. Fill the 9 x 9 grid with the digits 1 to 9.
2. Each row contains the digits 1 to 9 once.
3. Each column contains the digits 1 to 9 once.
4. Each of the nine 3 x 3 boxes contains the digits 1 to 9 once.
5. Each of the two long diagonals contains the digits 1 to 9 once.

There are 29 groups of nine cells to satisfy: 9 rows, 9 columns, 9 boxes and 2 diagonals. A puzzle gives you some digits at the start, and there is exactly one way to complete it. You never need to guess or to calculate.

Finding the two diagonals

The first diagonal runs from the top left cell, row 1 column 1, to the bottom right cell, row 9 column 9. The second runs from the top right cell, row 1 column 9, to the bottom left cell, row 9 column 1. They cross at the centre of the grid, row 5 column 5. In the LogikLand book both diagonals are shaded light grey on every page, so you do not have to count.

An example you can check

Read the diagonals of the solution from top to bottom:

• Top left to bottom right: 9, 7, 8, 5, 4, 3, 1, 6, 2. The nine digits, once each.
• Top right to bottom left: 5, 9, 6, 1, 4, 2, 7, 8, 3. Again the nine digits, once each.
• Both lists have a 4 in the fifth place. That is the centre cell, shared by the two diagonals.

The diagonal rule is not optional

A beginner sometimes asks whether the diagonals are only a decoration. They are not. We took LogikLand Sudoku X grids and asked a solver to count their solutions when it ignores the diagonals. The answer, for 30 grids at each level:

In other words, the givens alone do not fix the grid: the diagonals do the rest. If you finish a row, a column and a box correctly but your diagonal repeats a digit, the grid is wrong.

Three common mistakes

• Checking the diagonals only at the end. By then an error may be buried under twenty digits. Look at the grey cells each time you write a digit that is on a diagonal.
• Treating the centre as an ordinary cell. It lies on both diagonals, so it must differ from the digits of its row, column, box and both diagonals.
• Counting the diagonal cells wrongly. Each diagonal has nine cells. The centre cell is counted in both, which is why the two diagonals together cross 17 cells, not 18.

How LogikLand builds a Sudoku X

1. It fills a complete grid that respects all 29 groups, diagonals included.
2. It removes digits two at a time, in symmetric pairs, as long as the solution stays unique, and it stops at the minimum number of digits for the level.
3. It rates the grid by the hardest technique needed to solve it, and keeps it only if that matches the level.
4. It checks the final grid again with a separate search for exactly one solution.

The four levels

In a book

The Sudoku X assistant works with a free account. You choose the page size (8.5 x 11 or 6 x 9 inches), one level or several, the number of puzzles, 1, 2 or 4 grids per page, and 1, 2, 4 or 6 solutions per page. Each title can show the name, the level and the number, the name and the number, the level and the number, or the number alone. The rules page can be a detailed guide, a short page or left out. If you mix levels, the grids appear from the easiest level to the hardest. Books made on the FREE plan are for personal use, and commercial rights come with the PRO and EXPERT plans.

Questions