Fortress Sudoku: Rules and Solving Strategy

Read every fortress comparison correctly

Fortress Sudoku keeps the normal rule that every row, column, and 3x3 box contains 1 through 9 exactly once. In the common version, each shaded cell must contain a digit greater than every orthogonally adjacent white cell. Orthogonal means directly above, below, left, or right, not diagonally. A shaded cell beside a white 6 must therefore be 7, 8, or 9. A white cell beside a shaded 4 must be 1, 2, or 3. The comparison applies separately to every qualifying neighbor. If shaded cells touch, many puzzles do not compare them with each other because the rule names adjacent white cells; always follow the wording supplied with the individual puzzle. Edge and corner cells naturally have fewer neighbors. Shapedoku itself uses classic 3x3 boxes and glowing shapes without numerical size, so Fortress is a numbered variant rather than a mode in the standard game. Its logic still depends on the same disciplined candidate maintenance used in Hard and Extreme Sudoku.

Convert inequalities into upper and lower bounds

Treat every shaded-white contact as a simple inequality. The shaded candidate must be above the white candidate, and the white candidate must be below the shaded candidate. Broad bounds are useful even before either cell is solved. If a shaded cell can only be 5, 6, or 7, every adjacent white cell is limited to digits below at least one surviving shaded value, but you must preserve compatible pairs rather than applying the weakest bound carelessly. A white 6 would remove 5 and 6 from the shaded cell, leaving 7. Conversely, if an adjacent white cell is restricted to 1, 2, or 3, it may not narrow a shaded cell that already holds 6, 7, or 8. Compare candidate pairs directly. Remove a candidate from one side when no candidate on the other side can satisfy the inequality. This support test is safer than assuming that shaded always means very high and white always means very low. A shaded cell can be 4 when all relevant neighbors are below 4.

Follow chains of neighboring comparisons

Several fortress contacts can combine into a local network. A shaded cell touching three white cells must be greater than all three, so its lowest candidate must exceed at least one legal candidate in each neighbor. If one white neighbor becomes 7, the shaded cell is restricted to 8 or 9, which may force another digit elsewhere in its row or box. A white cell touching two shaded cells must be lower than both, so a low upper bound from either side can eliminate candidates. Standard units make these networks stronger. Suppose a shaded cell and two of its white neighbors lie in one box. They cannot repeat, and their order is partly known. If the three cells are restricted to 3, 4, and 5, the shaded cell must be 5, while the white cells take 3 and 4. After every inequality result, rescan the affected row, column, and box for singles or subsets. Fortress puzzles become manageable when comparisons are treated as candidate filters, not as invitations to guess which cells look high.

1. Mark every orthogonal shaded-white contact as a greater-than relationship.
2. Remove a candidate when it has no compatible value in the neighboring cell.
3. Use placed white digits to raise the minimum of adjacent shaded cells.
4. Use placed shaded digits to lower the maximum of adjacent white cells.
5. Combine inequalities with no-repeat rules inside rows, columns, and boxes.
6. Rescan all affected units after one comparison becomes exact.