Anti-Knight Sudoku

The stored puzzles have the fewest givens of any 9×9 board here after killer, between 13 and 20, and the board offers four levels, Easy to Expert.

What does the knight’s-move rule forbid?

Pick any cell. Count two steps along a row or column and one step sideways. Every cell you can land on that way is a knight’s move away, and none of them may hold the same digit as the cell you started from. In the middle of the board that is eight cells. Near an edge or corner there are fewer, because some moves fall off the board. The small grid on the rules page shows the eight positions, and the controls page covers input.

The rule is a restriction between pairs of cells, not a new group of nine. That changes how you use it: you will be crossing out a digit from the cells at a knight’s distance from every placement, not looking for a digit in a new house.

How many cells does a cell see?

A classic cell has twenty peers. On this board:

• A corner cell still has twenty, because the two knight moves from a corner land in its own box.
• A cell next to a corner, such as row 1, column 2, has twenty-one.
• A cell in the middle of the board, such as row 5, column 5, has twenty-eight, the most of any cell.

So a digit placed near the center clears itself from eight more cells than the classic rules would, while a digit in a corner clears no extra ones.

What are the puzzles like?

There are 150 stored puzzles at each of Easy, Medium, Hard and Expert, and no Evil. The givens run from 13 to 20, averaging 16.3 to 16.7. That is about eight fewer than a classic puzzle, and it is a sharp drop. Every puzzle has exactly one solution, confirmed by the same check as on every other board. The generator found no puzzle that needed more than Expert-level techniques, so the board has no Evil level.

Which techniques does it need?

In the stored data, with 150 puzzles per level:

• Medium: pointing pairs in 96% of puzzles, box/line reduction in 44%, naked pairs in 30% and hidden pairs in 21%.
• Hard: naked triples in 73% and X-Wing in 31%.
• Expert: simple coloring in 84% and XY-Wing in 65%, with Swordfish in 3%.

The Expert profile is close to the diagonal board’s, with coloring dominant, but XY-Wing is much more prominent here at 65%, against 44% on the diagonal board. If you want to be ready for Expert, learn XY-Wing and simple coloring. Note that the site’s technique solver treats a knight’s-move pair as a two-cell restriction, so its hints and its grading take the knight rule into account.

How do you remember the rule while solving?

This is the board where players most often break its own rule. The knight’s move is easy to overlook, since it does not form a line you can follow with your eye. Some habits help:

1. Select before you place. With highlighting on, the game shades the cells your selection sees, and that includes the knight’s-move cells.
2. Check eight cells, not twenty. After you place a digit, run through the eight knight positions once and remove the digit from their notes. Automatic note removal does this for you if it is on.
3. Look for cells where the knight rule leaves one candidate. A cell can look open for a digit by row, column and box and still be blocked by a knight’s move. Those are the naked singles that classic habits miss.
4. Use notes. The knight rule produces many small eliminations, which are easiest to track as pencil marks. See the pencil marks guide.

What goes wrong?

The most common mistake is placing a digit in a cell that is a knight’s move from the same digit. With feedback on, the game flags that conflict. The common mistakes guide lists the variant-specific slips and how to trace them when they surface late.

Where does it sit among the variants?

Compared with hyper and diagonal, which add houses to scan, this board adds a rule about pairs of cells and so feels different. If you prefer a rule with arithmetic, try killer. The games hub lists every board, and how Sudoku difficulty is graded explains what the levels mean.