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Anti-king is on, and a box border runs down the middle. Can the highlighted cell be a 7?
Level 4 · Whole-grid rules
How to solve anti-king sudoku
Cells a king’s move apart, including diagonally, can’t hold the same digit.
Anti-king sudoku adds one rule to the whole grid. Two cells that touch, even only at a corner, can't hold the same digit.
Cells that share an edge are already in the same row or column, and cells inside one box already differ. The rule adds something new only for diagonal neighbors on opposite sides of a box border.
How setters write it
The same rule, worded the ways you’ll see it on puzzles.
- Cells separated by a king’s move cannot contain the same digit.
- Anti-king.
Worth memorizing
- It only matters across box borders. Inside a box, digits never repeat anyway.
- Diagonal touches across a border are the ones to check.
Solving tips
Check diagonals across borders
A 7 on the right edge of a box rules out 7 in the cells diagonally up-right and down-right of it, in the next box.
Box corners reach furthest
A digit in a box corner touches three other boxes. A 4 in the bottom-right cell of the top-left box rules out 4 from one cell in each of the three boxes it touches.
Pairs block the cells beside them
If a 5 must go in one of two stacked cells on a box's right edge, the two cells directly to their right can't be 5. Each of them touches both options.
Scan singles with extra crosses
Scan each digit for singles as usual, and also cross off the diagonal neighbors of every copy across box borders. A digit in a box corner removes up to three extra cells.
A worked example: finding the 7 in the top-left box
Anti-king is on. We name cells by row and column, so row 2, column 4 is r2c4. The top-left box is empty. There is a 7 in r2c4 and another 7 in r4c1. Where does the top-left box put its 7?
- The 7 in r2c4 shares row 2 with the box. So r2c1, r2c2 and r2c3 can't be 7.
- r2c4 touches r1c3 and r3c3 at their corners. Those two cells are in the top-left box, just across the border from the 7. Neither can be 7. Four cells are left: r1c1, r1c2, r3c1 and r3c2.
- The 7 in r4c1 shares column 1 with the box. So r1c1 and r3c1 are out. Two cells are left: r1c2 and r3c2.
- r4c1 touches r3c2 at a corner, across the border below the box. So r3c2 can't be 7.
- Only r1c2 is left, so it is the 7. Check it. r1c2 is 1 row and 2 columns from r2c4, so the two cells don't touch. It is 3 rows from r4c1, so those don't touch either.
Practice
Reference table
| Cell in the center box | Left column | Middle column | Right column |
|---|---|---|---|
| Top row | 3 | 2 | 3 |
| Middle row | 2 | 0 | 2 |
| Bottom row | 3 | 2 | 3 |
Going deeper
Every 2x2 square works like a small region
Take any 2x2 square of cells. Each cell touches the other three, either along an edge or at a corner. So under anti-king, the four cells must hold four different digits.
This is most useful when the square crosses a box border. For example, r3c3, r3c4, r4c3 and r4c4 sit in four different boxes. Normal rules would let r3c3 and r4c4 match. Anti-king does not. When three cells of such a square are known, the fourth can't be any of those three digits.
You can use the square with candidates too. If r3c3 and r4c4 must hold 1 and 2 in some order, then r3c4 and r4c3 can't be 1 or 2. Each of those two cells touches both r3c3 and r4c4, so it touches the 1 and the 2 wherever they end up.
How a digit on a box edge clears a column
Put a digit in the middle cell of a box's right column, like r2c3. In the box to its right, r2c4 is out because it shares row 2. r1c4 and r3c4 touch r2c3 at a corner, so they are out too. The whole left column of the next box is gone.
The same thing happens on every side. A digit in the middle of a box's bottom row clears the top row of the box below it. Once you spot this, one placed digit can push the next copy into a much smaller area.
Corners reach three boxes
A digit in a corner cell of the center box touches cells in three other boxes, as the table shows. For example, r4c4 touches r3c3 in the top-left box, r3c5 in the top-middle box and r5c3 in the middle-left box. Each of those loses that digit.
The center cell of a box touches only cells in its own box, so it adds nothing new. When you scan a digit, look first at copies sitting in box corners.
Common mistakes
Missing touches at the corners
Beginners check cells that share an edge and forget cells that touch only at a corner. Edge neighbors are already in the same row or column, so they rarely matter. The corner touches across a box border are where the rule does its work.
Reading it as a ban on digits one apart
Anti-king bans the same digit on touching cells. It says nothing about 4 next to 5. That is a different rule called non-consecutive. Read the puzzle's rules to see which one applies.
Checking only one neighboring box
A digit in a box corner touches three other boxes. It is easy to cross off the cell in one box and forget the other two. Go around all four corners of the cell each time.
In mixed-rule puzzles
Anti-king often appears with anti-knight. Together they rule out a digit from every cell that touches it and every cell a knight's move away, which leaves few spots for its next copy in the nearby boxes. With non-consecutive, touching cells can't repeat a digit, and cells that share an edge also can't be one apart. On a marked diagonal, the cells along the diagonal touch each other at corners, but the diagonal rule already bans repeats there, so anti-king adds nothing along that line. It does add limits between the diagonal and the cells beside it. With killer cages, anti-king can rule out a repeat between two separate cages whose cells touch at a corner.
What the video shows
- Cells a chess king’s move apart, including diagonally, can’t hold the same digit. It matters across box borders.
- These 7s touch diagonally across the border.
- Different digits are fine.
Questions solvers ask
What is anti-king sudoku?
A sudoku where cells a chess king's move apart, including diagonally, can't contain the same digit.
Does anti-king apply to cells side by side?
Yes, but cells side by side already share a row or column, so normal rules cover them. The new limits come from diagonal touches.
Why does anti-king only matter across box borders?
Inside a box every digit is already different. Only diagonal neighbors in two different boxes gain a new limit.
What is the difference between anti-king and non-consecutive sudoku?
Anti-king bans the same digit on touching cells, including diagonals. Non-consecutive bans digits one apart on cells that share an edge.
Is anti-king the same as no-touch sudoku?
Setters usually use no-touch for the same idea: the same digit can't appear in touching cells, even at a corner. Some puzzles use the name for a different rule, so read the rules.
Can the same digit touch diagonally in normal sudoku?
Yes. In normal sudoku, the same digit can sit in two cells that touch at a corner, as long as they are in different boxes. Anti-king is the rule that stops it.
Does anti-king wrap around the edge of the grid?
No. Cells only touch inside the grid. A cell on the left edge does not touch a cell on the right edge unless the puzzle says the grid wraps.
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