Fortress Sudoku

Fortress Sudoku shades certain cells as "fortresses". The rule is a simple comparison: a fortress cell must be strictly greater than each of its orthogonal neighbours — the cells directly above, below, left and right of it. A fortress towers over everything it touches, which quietly forces large digits into the shaded cells and small ones around them.

The rule: a fortress beats its neighbours

Wherever a cell is shaded as a fortress, every cell sharing an edge with it must hold a smaller digit. Below, the shaded fortress holds 7, and its four neighbours (3, 5, 2 and 4) are all below it.

A worked example, step by step

Take a shaded fortress whose upper neighbour is already a 6.

Step 1 — the fortress must beat the 6. A fortress is larger than every neighbour, so it must be greater than 6. That leaves only 7, 8 or 9.

Step 2 — the neighbours shrink too. Whatever the fortress turns out to be, its other three neighbours must all be smaller than it — so they are pulled toward the low digits. One comparison tightens five cells at once.

Reading fortresses both ways

The rule cuts in two directions. A fortress cell can never be a 1 (nothing is smaller for its neighbours to be), and rarely a low digit at all — it needs room beneath it. Conversely, a large digit sitting next to a fortress is impossible: a 9 beside a fortress would have to be smaller than it, which cannot happen. So fortresses push high digits into the shaded cells and keep them out of the cells around them.

Solving strategy

• Start where a neighbour is known. A known neighbour puts a hard floor under the fortress (greater than it) and a ceiling over the others.
• Push the extremes. Fortresses gravitate to 8s and 9s; their neighbours gravitate to 1s and 2s.
• Rule out large neighbours. No neighbour of a fortress can be as large as the fortress — often that removes a 9 or 8 immediately.
• Feed the grid. Each digit a fortress fixes behaves like a given for its row, column and box.

Common mistakes

• Including diagonals. A fortress must beat its four orthogonal neighbours only, not the diagonal ones.
• Allowing a tie. The fortress is strictly greater — equal values are impossible anyway, but never treat a neighbour as "up to" the fortress.
• Making a fortress too small. A fortress needs smaller digits all around it, so it can't be a 1 and is rarely low.
• Forgetting ordinary Sudoku. Fortress cells still obey their row, column and box.

Can I play it here?

Not yet — Fortress 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:

• Browse all the Sudoku variants we do offer.
• Or print free puzzles from the printable PDF page.