All Sudoku Variants
9×9 · Constraint

Anti-Queen Sudoku

Also known as Queen's Move Sudoku

Chosen digits — most often the 9s — may not lie a queen's move apart along the grid's diagonals.

9

An example Anti-Queen puzzle (on the 9s): no two 9s may share a diagonal — the shaded diagonals through this 9 are barred to every other 9.

Anti-Queen Sudoku adds a chess rule for one or more chosen digits — most often the 9s. Those digits may not lie a queen's move apart: a queen slides any distance along a row, a column or a diagonal, so no two of the chosen digit can share a diagonal (rows and columns are already covered by ordinary Sudoku). In practice it is a powerful diagonal constraint on the marked digit.

The rule: the chosen digit can't share a diagonal

Take the marked digit — say 9. Ordinary Sudoku already stops two 9s sharing a row or column; the anti-queen rule adds that they can't share a diagonal either. Below, the central 9 forbids a 9 on every diagonal cell around it (red).

9 ✗9 ✗9 ✗9 ✗9 ✗9 ✗9 ✗9 ✗9

The central 9 forbids a 9 on both of its diagonals — the queen's diagonal reach.

A worked example, step by step

Suppose a 9 is placed, and a box further down the same diagonal still needs its 9.

Step 0. A 9 sits in the grid (above). Its two diagonals now carry the anti-queen ban.

Step 1 — the diagonal cells lose their 9. Every cell along either diagonal from the 9 can no longer be a 9 — including cells in far-off boxes that ordinary Sudoku would leave open.

9 ✗9 ✗9 ✗9 ✗9

Step 1. A 9 in the corner rules the 9 off its whole diagonal.

Step 2 — the target box is forced. With the 9 banned from the diagonal cells, a box the diagonal passes through often has only one legal home left for its 9 — a hidden single the plain rules could never produce.

Which digits, and how strong

Most Anti-Queen puzzles apply the rule to a single digit (the 9), because applying it to all nine would be extremely restrictive. The chosen digit becomes far easier to place, since each one you find clears two whole diagonals of that value. If a puzzle marks two digits (say 8 and 9), treat each independently — the ban only relates copies of the same digit.

Solving strategy

  • Track the marked digit's diagonals. Each placed copy clears both of its diagonals of that digit.
  • Hunt hidden singles. The extra diagonal reach often leaves a box only one home for the marked digit.
  • Remember it's a same-digit rule. The ban relates two copies of the chosen digit, not different values.
  • Feed the grid. Each marked digit placed behaves like a given for its row, column and box.

Common mistakes

  • Applying it to every digit. Usually only the marked digit (often 9) obeys the queen rule — check the puzzle.
  • Only checking short diagonals. A queen's reach is the whole diagonal, across box borders.
  • Relating different digits. The ban is between copies of the same digit, not between, say, a 9 and an 8.
  • Forgetting ordinary Sudoku. Rows, columns and boxes still apply to every digit.

Can I play it here?

Not yet — Anti-Queen Sudoku isn't one of the puzzle types SudokuStreak generates for now. But you can learn its rules above, and there's plenty here to sink your teeth into meanwhile: