Six visual techniques that separate solvers from grandmasters.
You know the four-phase method. You can clear Beginner and Medium puzzles without breaking a sweat. But the 9×9 and 10×10 boards keep stopping you cold.
These six techniques are the patterns expert solvers recognize instantly. Each one is illustrated with a mini board so you can see exactly how the logic works.
When you place a queen, it blocks its own column plus both adjacent diagonal cells in neighboring rows. That's 3 contiguous columns gone from each adjacent row — over a third of the board on an 8×8 grid.
Queen at R4C4 blocks columns 3–5 in rows 3 and 5 (red). Five columns survive in each adjacent row (blue).
Look at rows 3 and 5. The queen at R4C4 wipes out columns 3, 4, and 5 from both adjacent rows — column 4 from the column constraint, columns 3 and 5 from the diagonal constraint. That's 3 of 8 columns gone instantly.
Two queens compound this effect. If a second queen landed near column 7, the overlapping shadows would leave rows 3 and 5 with only 2–3 candidates each.
When a revealed 2 has one queen already placed in its row, the second queen can only go in the corners of the clue's neighborhood that are on the opposite side — and diagonally away from the first queen.
The "2" (purple) has one queen to its left. The queen's column blocks C4; its diagonals block C3 and C5 in rows 3 & 5. Only R3C6 and R5C6 survive (blue) — the opposite corners.
The queen at R4C4 is adjacent to the "2" at R4C5, satisfying one of the two required neighbors. Now trace what it blocks among the "2"'s other neighbors: column C4 eliminates R3C4 and R5C4, the diagonals eliminate R3C3, R3C5, R5C3, and R5C5, and the row constraint eliminates R4C6.
Of the seven remaining neighbors, only R3C6 and R5C6 survive — both on the far side, diagonally away from the queen. The second queen must be one of these two.
When two queens are in rows r and r+2 with columns close together, the sandwiched row r+1 gets hit by overlapping shadows. Each queen blocks 3 columns in that row, and when they overlap, nearly everything is eliminated.
Row 4 is pinched: R3's queen blocks C2–C4, R5's queen blocks C5–C7. Only C1 and C8 survive (blue).
The queen at R3C3 blocks columns 2, 3, and 4 in row 4 (diagonal, column, diagonal). The queen at R5C6 blocks columns 5, 6, and 7 in row 4 (diagonal, column, diagonal). The labels show which queen causes each elimination.
Net result: 6 of 8 columns in row 4 are eliminated. Only the two outermost columns survive. One additional constraint narrows it to a single forced queen.
Zeros create 8-cell exclusion zones. When a "0" is close to a "2", their neighborhoods overlap — and the 0's exclusion zone wipes out cells that the "2" was counting on. The "2" goes from 5+ candidates to just 2, both forced as queens.
The "0" (purple) eliminates all 8 neighbors (red ×). Three of these — R3C5, R4C5, R5C5 — overlap with the "2"'s neighborhood. Only 5 candidates remain for the "2" (blue).
Start with the "0" at R4C4. Eliminate all 8 neighbors — that's R3C3–C5, R4C3, R4C5, R5C3–C5. Now look at the "2" at R4C6. Its neighbors are R3C5, R3C6, R3C7, R4C5, R4C7, R5C5, R5C6, R5C7.
Three of those — R3C5, R4C5, R5C5 — were already killed by the "0". The "2" goes from 8 neighbors to just 5 viable candidates, all on the right side of the board. Additional constraints (column queens, diagonals) typically narrow these 5 down to the exact 2 queens the "2" requires.
When you've placed most queens, only a few rows and columns still need them. Write out the remaining row/column intersections and cross off any blocked by diagonals. The valid assignment is often uniquely determined.
| C3 | C5 | |
|---|---|---|
| R5 | ♕ | × |
| R7 | × | ♕ |
R5C5 blocked by
R4C6 diagonal
6 of 8 queens placed. Rows 5 & 7 remain, columns 3 & 5 remain. The matching table reveals the only valid assignment.
With 6 of 8 queens placed, only rows 5 and 7 need queens, and only columns 3 and 5 are unsatisfied. Build the 2×2 matching grid and check each intersection for diagonal conflicts.
R5C5 is diag-adjacent to the queen at R4C6 — blocked. So R5 must use C3, which forces R7 to C5. Two queens resolved in seconds.
When a revealed "1" has only two possible neighbors left, one of them must be the queen. This binary choice propagates — each option locks a column, which eliminates candidates in other rows, potentially forcing more queens.
The "1" (purple) has only two candidates left: A at R4C6 and B at R6C4 (blue). One must be queen.
The "1" at R5C5 needs exactly one queen among its neighbors. Most have been eliminated (×). Only cells A (R4C6) and B (R6C4) remain. This gives you a powerful logical fork:
If A is the queen (R4C6):
Column 6 is done. Row 4 is done. Diagonals from R4C6 block R3C5, R3C7, R5C5 (revealed), R5C7. Trace what this forces in the remaining rows…
If B is the queen (R6C4):
Column 4 is done. Row 6 is done. Diagonals from R6C4 block R5C3, R5C5 (revealed), R7C3, R7C5. Trace the consequences…
If one branch reaches a contradiction (a row with no valid cells, a number that can't be satisfied), that candidate is eliminated. The other must be the queen.
Even if neither contradicts immediately, both branches propagate column and row constraints that may force other placements. Sometimes you can find a cell that's forced in both branches — that cell is guaranteed regardless.
These six patterns cover the vast majority of deductions needed for Grandmaster-level puzzles. Once you see them in practice, you'll recognize them instinctively.
The board talks to you — every queen placement creates shadows, every clue narrows the field. Learn to listen.
Play Today's Puzzle