Anti-King Sudoku: Rules and Solving Strategy

Understand what the anti-king rule actually adds

Anti-King Sudoku keeps all classic rules: every row, column, and 3x3 box contains the digits 1 through 9 once. It then forbids equal digits in any two cells that are a chess king's move apart. A king moves one square horizontally, vertically, or diagonally. Horizontal and vertical equality is already impossible in classic Sudoku because those cells share a row or column. The important new restriction is therefore diagonal adjacency. If a 6 is placed in one cell, the four diagonally touching cells cannot contain 6, in addition to the normal row, column, and box eliminations. At edges and corners there are fewer diagonal neighbors, but the rule is unchanged. Shapedoku does not currently use chess constraints, yet the same logic can be imagined with its symbols: if the heart were subject to anti-king rules, another heart could not sit diagonally beside it. This makes the variant easy to understand even though its candidate map becomes noticeably tighter.

Use 2x2 squares as quick visual units

A useful consequence is that every 2x2 block of cells must contain four different digits. Orthogonally adjacent cells are different because of rows and columns, while the two diagonal pairs are different because of the anti-king rule. This gives you a compact visual structure that classic Sudoku does not have. If three cells of a 2x2 block contain 2, 5, and 8, the fourth cannot use any of those values even when some of them would otherwise survive its row, column, and box. The same idea helps candidate scanning. When following one digit through adjacent rows, its possible columns cannot sit next to each other. If a 7 is in column 4 of one row, the rows immediately above and below cannot place 7 in columns 3, 4, or 5. Column 4 is already excluded by standard Sudoku, while columns 3 and 5 are the extra anti-king effect. These widened exclusion zones often create hidden singles inside nearby boxes.

Scan neighboring rows and boxes together

Anti-King Sudoku rewards scanning by digit rather than only by cell. Choose one digit and mark every placed occurrence. For each occurrence, mentally shade its row, column, box, and diagonal neighbors. Then inspect the neighboring boxes for positions that survive all four sources of restriction. Patterns across two adjacent rows are particularly useful. Suppose one box has two candidate positions for 4 on adjacent rows. A placed 4 just outside the box may eliminate one candidate through diagonal contact even though it does not share the box, row, or column with that cell. This is the kind of elimination classic Sudoku habits can overlook. Accurate Notes help on harder puzzles because a candidate may be legal under the three standard units but illegal under the king move. After each placement, clean the diagonal neighbors before searching for pairs or chains. Many standard techniques still work, but their candidate map must already include the anti-king restriction. If the notes are correct, familiar singles and subsets often do more work than exotic methods.

1. Apply normal row, column, and 3x3 box eliminations first.
2. For every placed digit, remove the same digit from all diagonally adjacent cells.
3. Use each 2x2 area as a quick check that all four digits are different.
4. Scan the same digit across neighboring rows and watch for one-column diagonal exclusions.
5. Update anti-king candidates before looking for pairs, triples, or chains.
6. When stuck, rescan by digit because the added diagonal pressure is easier to see globally.