How to Solve Sudoku Variants: Beginner Strategies

The good news about solving Sudoku variants is that you do not start again from zero. Every variant is a classic Sudoku with one rule changed, so the method is the same, and what you must learn is where to look. This article gives one routine for all variants, then shows the key move of Sudoku X and Jigsaw Sudoku on real grids, checked against the printed puzzle.

One routine for every variant

1. List the groups that each digit must appear in once: rows, columns, and the groups specific to the variant.
2. Take a digit that appears many times in the grid, and see where it can still go in each group.
3. When a digit has only one possible cell in a group, write it. This is the technique called the only place for a digit.
4. Repeat with the next digit, and only then switch to pencil marks for the cells that stay open.

Group by group, the difference between variants is only step 1. That is why it is worth reading the rules of the four variants once before you solve.

Sudoku X: sweep the diagonals

In Sudoku X, the two long diagonals are groups like any row. The most common mistake is to ignore them. Here is an easy grid, with its solution.

The digit 2 on the anti-diagonal

Look at the diagonal that runs from the top right (R1C9) to the bottom left (R9C1), where R1C9 means row 1, column 9. Only two cells of it are filled: R2C8 holds 1 and R8C2 holds 7. The digit 2 is missing, and we ask where it can go among the empty cells:

• R3C7: there is a 2 in its row, at R3C5.
• R4C6: there is a 2 in its column, at R8C6.
• R5C5: there is a 2 in its column, at R3C5.
• R6C4: there is a 2 in its row, at R6C1.
• R7C3: there is a 2 in its row, at R7C2.
• R9C1: there is a 2 in its column (R6C1) and in its box (R7C2).

Only R1C9 is left, and its row, column and box have no 2. So R1C9 is a 2. A solver who looks only at rows, columns and boxes does not see this cell at once: for the classic rules, R1C9 could still be 2, 8 or 9. We checked this example against the puzzle with a script.

Jigsaw Sudoku: follow the regions

In a Jigsaw Sudoku, the thick lines are the groups. Trace each region with a pencil first: a region is a group of nine cells that may wind through the grid. Here is a medium grid with its solution.

The digit 1 in the central region

Take the region around the centre of the grid. It has nine cells: R3C5, R3C6, R4C5, R4C6, R5C4, R5C5, R6C4, R6C5 and R6C6. It already holds a 9 (R3C5), a 7 (R5C4) and a 3 (R6C6), and is missing a 1, among others. Where can the 1 go?

• R3C6 and R4C6: there is a 1 in their column, at R5C6.
• R5C5: there is a 1 in its row, at R5C6.
• R6C4 and R6C5: there is a 1 in their row, at R6C1.

Only R4C5 is left, so it is a 1. This is the same move as in classic Sudoku, but applied to a region whose shape you have to read from the thick lines.

Killer Sudoku: add before you place

Killer Sudoku is the variant where the routine changes the most, because the first digits come from addition. Start with cages of one cell, the sums that have only one answer, and the rule that every box, row and column adds up to 45. The full method, with a real grid, is in how to solve Killer Sudoku.

The four steps of difficulty

The LogikLand generators for Sudoku X and Jigsaw grade each grid by the hardest technique a person needs to solve it. This is what the grades mean, and which levels use them.

In other words, an easy or medium Sudoku X or Jigsaw can be finished with the move shown above and nothing else. If you feel stuck on an easy grid, the answer is almost always a diagonal or a region that you have not checked yet.

Mistakes that cost the most time

• Forgetting a diagonal. In Sudoku X, the centre cell is on both diagonals and has the strictest constraints.
• Reading a region wrongly. Trace its outline with a pencil, as if colouring it in.
• Placing a digit without checking all groups. One wrong digit leads to others.

When you want a full book, the Sudoku and Variants assistant puts these grids in one book. Create a free account to use it, and see the Sudoku book generator page for classic Sudoku. For harder grids, read advanced Sudoku variants techniques.

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