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Anti-knight is on. Can the highlighted cell be a 6?
Level 4 · Whole-grid rules
How to solve anti-knight sudoku
Cells a chess knight’s move apart can’t hold the same digit.
Anti-knight sudoku adds one rule to the whole grid. Two cells a chess knight's move apart (two steps one way and one step to the side) can't hold the same digit.
Inside a box, digits already can't repeat, so the rule does its work where it reaches into neighboring boxes. Each placed digit rules out a few extra cells beyond its row, column and box.
How setters write it
The same rule, worded the ways you’ll see it on puzzles.
- Cells separated by a knight’s move (in chess) cannot contain the same digit.
- Anti-knight.
Worth memorizing
- It reaches into neighboring boxes, which is where it bites.
- In a box, a digit on the edge rules out two or three cells in each neighboring box.
Solving tips
Trace the L shapes
From a placed digit, trace two cells across and one down, or one across and two down, in every direction. If any L lands on the same digit, the placement is wrong.
Count the knight's reach
A cell near the middle of the grid has eight cells a knight's move away. A corner cell of the grid has only two.
Check the box next door
A 6 in the top-right cell of a box rules out two cells in the box to its right, on top of the three in its row. Only four cells in that box can still hold a 6.
Hit both cells of a pair
If a digit can only go in two cells of a box, any cell a knight's move from both of them can't hold that digit.
A worked example: finding the 6 in the top-left box
Anti-knight is on. We name cells by row and column, so row 2, column 5 is r2c5. The top-left box is empty. There is a 6 in r2c5 and another 6 in r5c2. Where does the top-left box put its 6?
- The 6 in r2c5 shares row 2 with the box. So r2c1, r2c2 and r2c3 can't be 6. Six cells are left: r1c1, r1c2, r1c3, r3c1, r3c2 and r3c3.
- From r2c5, one row up and two columns left is r1c3. One row down and two columns left is r3c3. Both are a knight's move from the 6, so both are out. Four cells are left: r1c1, r1c2, r3c1 and r3c2.
- The 6 in r5c2 shares column 2 with the box. So r1c2 and r3c2 are out. Two cells are left: r1c1 and r3c1.
- From r5c2, two rows up and one column left is r3c1. That is a knight's move, so r3c1 can't be 6.
- Only r1c1 is left, so it is the 6. Check it. r1c1 is 1 row and 4 columns from r2c5, and 4 rows and 1 column from r5c2. Neither is a knight's move, so the 6 is safe.
Practice
Reference table
| Column 1 | Column 2 | Column 3 | Column 4 | Column 5 | |
|---|---|---|---|---|---|
| Row 1 | 2 (0) | 3 (1) | 4 (2) | 4 (2) | 4 (2) |
| Row 2 | 3 (1) | 4 (4) | 6 (4) | 6 (4) | 6 (6) |
| Row 3 | 4 (2) | 6 (4) | 8 (6) | 8 (6) | 8 (6) |
| Row 4 | 4 (2) | 6 (4) | 8 (6) | 8 (6) | 8 (6) |
| Row 5 | 4 (2) | 6 (6) | 8 (6) | 8 (6) | 8 (8) |
Going deeper
Why the new limits land in other boxes
A knight's move always changes both the row and the column. So two cells a knight's move apart never share a row or a column. The only normal rule they can share is the box.
That means the rule is strongest for cells whose knight's moves leave the box. The center cell of a box, like r5c5, reaches 8 cells and all 8 are in other boxes. A cell in a box corner, like r4c4, also reaches 8 cells, but 2 of them are inside its own box, so only 6 are new. The table shows these counts for every position near the top-left corner.
What one digit does to the box next door
Put a digit in the middle cell of a box's right column, like r2c3. In the box to its right, row 2 is out by the row rule. The knight's moves from r2c3 land on r1c5 and r3c5, the middle column of the next box. That leaves only the four corner cells of that box: r1c4, r1c6, r3c4 and r3c6.
Now put the digit in the center of a box, like r2c2. In the box to its right, row 2 is out again, and the knight's moves hit r1c4 and r3c4. The digit can only go in the middle or right column of that box, in row 1 or row 3. Learning these two shapes saves you from tracing every L by hand.
Placing a digit near the edge
Cells near the edge of the grid have fewer knight's moves. A corner cell like r1c1 reaches only 2 cells, and both are inside its own box, so the rule adds nothing there. A digit placed in a corner of the grid gives you no extra anti-knight help.
So when you look for anti-knight deductions, start with digits placed near the middle of the grid. They reach the most cells in other boxes.
Common mistakes
Tracing only four of the eight moves
A knight can move in eight directions: two up and one left, two up and one right, two down and one left, two down and one right, and the same with one and two swapped. Beginners often check the moves going right and down and forget the rest. Trace all eight each time you place a digit.
Mixing up a knight's move and a king's move
A knight's move is two cells one way and one cell to the side. It never lands on a cell that touches the start cell. If you are crossing off cells that touch the digit, you are solving anti-king by mistake.
Looking for help inside the box
Digits already can't repeat in a box, so knight's moves that stay inside the box tell you nothing new. The useful ones cross into a neighboring box. Spend your checking time on the cells across the border.
In mixed-rule puzzles
Anti-knight often appears with anti-king. Together they ban the same digit from every cell that touches it and every cell a knight's move away, so each placed digit rules out many cells in the boxes around it. Anti-knight also pairs with diagonals. A digit on a marked diagonal can't repeat on that diagonal, and its knight's moves reach cells on and near the other diagonal too. With killer cages, the rule can rule out digits inside a cage that spans two boxes. Two cells a knight's move apart in the same cage must hold different digits anyway, so the rule matters most for cages that are close but separate. Always check which rules the puzzle lists, since setters combine these in many ways.
What the video shows
- Cells a chess knight’s move apart can’t hold the same digit.
- This 6 is a knight’s move from the other.
- A different digit can go there.
Questions solvers ask
What is anti-knight sudoku?
A sudoku where cells a chess knight's move apart can't contain the same digit, on top of the normal rules.
What is a knight's move in sudoku?
It is an L shape: two cells in one direction and one cell to the side, like the knight in chess.
Does the anti-knight rule apply inside a box?
Yes, but digits never repeat in a box anyway. It only adds new information when the knight's move crosses into another box.
What is the difference between anti-knight and anti-king?
Anti-king bans the same digit on touching cells, including diagonals. Anti-knight bans it on cells an L-shaped move apart.
How many cells does a knight's move reach in sudoku?
Up to 8. A cell near the middle of the grid reaches 8 cells. Cells near the edges reach fewer, and a corner cell reaches only 2.
Does the anti-knight rule apply to given digits?
Yes. It applies to every digit in the grid, given or placed. A given 3 rules out 3 from every cell a knight's move away.
Is anti-knight sudoku harder than normal sudoku?
It adds a rule, which gives you more ways to rule out digits. That lets a puzzle start with fewer given digits. How hard a puzzle feels depends on the setter.
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