How to Solve Sudoku X

Sudoku X adds two units to the nine rows, nine columns and nine boxes: the two long diagonals, which also hold the digits 1 to 9 once each. Everything you know about classic sudoku still works. The extra work is to treat each diagonal as one more unit and to check it every time you place a digit on it. This page shows where the diagonals give the most, and why a Sudoku X can start with fewer givens than a classic puzzle. The rules are in What is Sudoku X?.

1. Treat each diagonal as a tenth unit

In a classic sudoku, every cell belongs to three units: a row, a column and a box. In Sudoku X, the sixteen other cells on the diagonals belong to four units, and the centre cell, which is on both diagonals, belongs to five. A digit placed on a diagonal removes that digit from eight more cells than it would in a classic puzzle.

So the first habit is simple. Whenever you place a digit on a shaded cell, go along the whole diagonal and remove that digit from every pencil mark on it. Whenever you look for where a digit can go, include the diagonal in the search.

2. Start at the centre

The centre cell is in the middle row, the middle column, the middle box and both diagonals. It is the most constrained cell in the grid. Collect the digits already placed in all five of its units. Often only one or two candidates remain, and in many puzzles the centre is the first cell you can fill.

The centre box as a whole is special too. Both diagonals pass through it, three cells each, and they cross at the centre. Five of the nine cells of the centre box are on a diagonal. Each diagonal's three cells in the centre box hold three different digits, and the other six cells of that diagonal, in the corner boxes, hold the remaining six.

3. Diagonals and corner boxes

Each diagonal passes through three boxes: a corner box, the centre box and the opposite corner box. It has three cells in each. If a digit already sits on the diagonal's cells in one corner box, that digit cannot appear on the diagonal in the other two boxes. Combined with the box rule, this often fixes where the digit goes in a corner box: not on the diagonal, so in one of the six off-diagonal cells, and the row and column then narrow those six.

The reverse is also useful. If a digit cannot go anywhere in a corner box except on the diagonal, then it is on the diagonal in that box, and it is barred from the diagonal cells of the centre box and the opposite corner box.

4. Hidden singles on a diagonal

Look at a diagonal and a digit. Cross out every diagonal cell whose row, column or box already contains that digit. If one cell is left, the digit goes there. This hidden single on a diagonal is the most frequent Sudoku X step, and it is the one classic solvers miss, because they scan rows, columns and boxes only.

Do the same check from the other side. For a digit that has few places left in a row, see whether one of those places is on a diagonal that already holds the digit. That place is out.

5. Pairs on a diagonal

Two cells on a diagonal that share the same two candidates form a pair, and those two digits are removed from the other seven cells of the diagonal. Because diagonal cells sit in different rows, columns and boxes, a pair on a diagonal often appears where no classic pair exists, and it can unlock a region that looked stuck.

6. Why the puzzle has fewer givens

A classic sudoku needs at least 17 givens to have one solution, and most published puzzles have 25 to 35. Sudoku X puzzles on this site start with 22 to 32 givens. The two diagonals provide the rest of the information. That is why you should use the diagonals from the first step. A Sudoku X solved as if the diagonals were decoration runs out of moves early, and the moves that remain all use the diagonals.

7. A solving order that works

  1. Fill in the centre cell if its five units leave a single candidate.
  2. For each digit 1 to 9, check both diagonals for a hidden single.
  3. Scan rows, columns and boxes as in a classic sudoku, but remove candidates along the diagonals as you go.
  4. Look for pairs on the diagonals and in the centre box.
  5. Repeat from step 2 after every few placed digits. The diagonals change with every digit placed on them.

8. Mistakes to avoid

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