Advanced Sudoku Variants Techniques for Harder Grids

At the hard level, a Sudoku X or a Jigsaw Sudoku has about 24 digits at the start, and the simple moves run out before the grid is full. That is where advanced techniques begin. The most useful one, locked candidates, is easy to understand, and in these variants it works in new ways: a group can be a diagonal or a region as well as a row, a column or a box. Both examples below come from real hard grids from the LogikLand generators and were checked by script.

Where the basics stop

The generators of these variants grade a grid by the hardest technique needed. Easy and medium grids need only the only-place technique. Hard grids also need cells with a single candidate (grade 1) or eliminations with aligned digits and pairs (grade 2). Expert grids need something beyond those. When you have filled in everything the first two methods can give you and you still have empty cells, it is time to write pencil marks and look for locked candidates.

If you are not yet comfortable with the basic moves, read how to solve Sudoku variants first.

Locked candidates between two groups

Take one group, say a box. Look at a digit that is not yet placed in it, and mark every cell where it could still go. If all of those cells also belong to a second group, for example one row, then the digit of the first group has to be in that row. So you can remove the digit from the other cells of the row. The rule works in both directions: if in a row the digit can only go in cells of one box, remove it from the rest of the box.

In Sudoku X: boxes and diagonals

On this grid, a script wrote in every digit that the only-place technique and the single-candidate technique can find: 19 digits, 38 cells still empty. At that stage, several locked-candidate moves are possible. We show the two that involve the diagonals.

From a box to the diagonal

In the bottom left box (rows 7 to 9, columns 1 to 3), the digit 3 can only go in R7C3 or R8C2. Both cells lie on the diagonal that runs from the top right to the bottom left. So the 3 of that diagonal is one of them, and no other cell of the diagonal can hold a 3. This removes 3 from R4C6 and R6C4, two cells of the same diagonal.

From the diagonal to a box

On the same diagonal, the digit 4 can only go in R4C6 or R6C4. Both cells are in the central box. So the 4 of the central box is on the diagonal, and R4C5, R5C4, R5C6 and R6C5 cannot be 4. We checked both moves against the solution: the digit is never removed from a cell where it belongs.

In Jigsaw: regions and lines

After the same preparation, only 6 digits can be found, and 50 cells are still empty. Many locked moves are available, and we show two.

From a row to a region

In row 5, the digit 8 can only go in R5C2 or R5C3. Both belong to the region made of R3C1, R4C1, R4C2, R4C3, R5C1, R5C2, R5C3, R6C2 and R6C3. So the 8 of that region is in row 5, and the other cells where it could have gone, R4C1, R4C2, R4C3, R6C2 and R6C3, are not 8.

From a region to a row

In the region made of R1C1, R1C2, R1C3, R2C1, R2C2, R3C2, R3C3, R3C4 and R4C4, the digit 1 can only go in R2C1 or R2C2. Both are in row 2, so the 1 of row 2 is in this region and R2C9 cannot be 1.

For Killer: sums as groups

The same idea of reasoning on groups applies to Killer Sudoku, with sums instead of digits: a box or a row adds up to 45, so the cages inside it tell you the cells left over. That is explained, with a verified hard grid, in advanced Killer Sudoku techniques.

A working method for hard grids

Writing pencil marks late saves time: on this Sudoku X, 19 digits were found before any note was needed. If you want to practise on a full book, create a free account and open the Sudoku and Variants assistant. The Sudoku book generator page covers classic Sudoku.

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