9x9 Queens Puzzle #166

Difficulty: easy. Place 9 queens on this 9x9 board so that no two share a row, column or color region and none touch — including diagonally. This puzzle has exactly one solution, and it has been verified solvable by deduction alone: the complete 10-step reasoning is written out below.

Previous puzzle · All 9x9 puzzles · Next puzzle

Step-by-step solution for puzzle #166

What follows is a complete solve of puzzle #166, worked the way a person works it rather than the way a computer does. It runs to 10 deductions — 9 queen placements and 1 elimination step that narrow the board between them. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the region shadow.

Techniques this board needs: last square in a region, region shadow.

Show the full walkthrough (5 steps) — contains the solution

  1. Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: mint has one square left, so its queen takes row 4, column 1; amber has one square left, so its queen takes row 2, column 2; pale yellow has one square left, so its queen takes row 7, column 9; khaki has one square left, so its queen takes row 8, column 6; orange has one square left, so its queen takes row 9, column 8; indigo has one square left, so its queen takes row 1, column 7. After each one, clear that row, that column, the rest of the colour and the ring of neighbours before looking for the next. The last of them seats the queen on row 1, column 7.

  2. Step 2. Wherever slate ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

  3. Step 3. The red region is down to one open square, at row 6, column 3. Every colour holds exactly one queen, so that square is forced. Row 6 and column 3 are now spoken for, along with the squares touching that queen.

    Puzzle #166 after step 3: 7 of 9 queens placed
    The board after step 3 — 7 of 9 queens placed.

  4. Step 4. Only row 5, column 5 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 5, the rest of the slate region and every square adjacent to it — diagonals included.

  5. Step 5. The blue region is down to one open square, at row 3, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 4, the remaining blue squares, and the ring of neighbours around row 3, column 4.

    Puzzle #166 after step 5: 9 of 9 queens placed
    The board after step 5 — 9 of 9 queens placed.

That completes the board: 9 queens seated, one in every row, one in every column and one in every colour, with no two of them touching. Notice that nothing in the sequence above required a guess — each placement followed from an elimination already on the grid, which is what “single solution, solvable by logic” actually means in practice.

About 9x9 Queens puzzle #166

Board #166 of the 9x9 bank carries a easy rating. Its 81 squares are shared between nine colored regions, and the solution places nine queens: one per row, one per column, one per region, none of them side by side or corner to corner.

As with every puzzle in this collection, #166 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.

How the colors divide this board

From smallest to largest, the regions on puzzle #166 are: mint (1 square), pale yellow (1 square), khaki (1 square), orange (7 squares), amber (8 squares), indigo (10 squares), blue (11 squares), red (20 squares), slate (22 squares). An even split would hand every color 9 squares, so the mint region is running 8 squares under that average while the slate region is the roomiest area on the grid with 22 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Mint has only 1 place to put its queen; slate has 22. The spread between them on this board is 21 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

A region's outline can constrain it more than its size does. Here mint is the most solid, filling 100% of its 1×1 box, and blue the most diffuse at 55% of its 5×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

Below is every color on #166 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.

Mint covers 1 square, spanning 1 row and 1 column (rows 4–4, columns 1–1). It never leaves row 4, so its queen is locked to that row.

Pale yellow occupies 1 square within rows 7–7, columns 9–9. It never leaves row 7, so its queen is locked to that row.

Khaki: 1 square across rows 8–8, columns 6–6. It never leaves row 8, so its queen is locked to that row.

Orange covers 7 squares, spanning 2 rows and 4 columns (rows 8–9, columns 6–9).

Amber occupies 8 squares within rows 1–5, columns 1–2.

Indigo: 10 squares across rows 1–3, columns 5–9.

Blue covers 11 squares, spanning 5 rows and 4 columns (rows 1–5, columns 2–5).

Red occupies 20 squares within rows 6–9, columns 1–6.

Slate: 22 squares across rows 3–7, columns 4–9.

Where to start on this board

Open on the tightest color. Here that is mint, confined to 1 square between rows 4 and 4 and columns 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #166.

Because mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. Then look at which colors just lost ground: on a grid this size that one observation usually forces a second region within a move or two.

Work outward to the other flat regions next. Pale yellow, khaki and orange are no more than two rows tall, so their queens are confined to a narrow band. When two flat regions overlap the same pair of rows, those rows are spoken for and every other color is locked out of both — the single most productive pattern in the game, and it is live on this board.

The tightest lines on puzzle #166

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 6 and 9 are the narrowest, touched by only 2 colors. Column 3 is the tightest column, with 2 colors.

Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 8 rows. By contrast row 4 meets 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.

Working through the middle game

The middle of #166 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.

Keep alternating between two views of the board. In the region view you ask which of the nine colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 9x9 board unwinds.

The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.

Why puzzle #166 is rated easy

What earns a board its rating is the shape of its opening. Here that opening offers six single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 21. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.

A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.

Techniques that work well at 9x9

At 9x9 a full re-scan after every move starts to get slow, so work locally instead. Once a queen goes down, check only the regions, rows and columns that placement actually touched — that is where new information appeared. Fall back to a complete sweep only when the local pass turns up nothing, and your solve times will drop noticeably.

One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #166 the place to look for one is around row 6.

As a sanity check rather than a spoiler: the finished solution to #166 puts 4 queens on the outer border and 5 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.

How to play Queens

  1. The board is an N×N grid divided into N colored regions.
  2. Place exactly one queen (♛) in each row, each column, and each colored region.
  3. No two queens may touch each other — not horizontally, vertically, or diagonally.
  4. Tap once to mark a square with an X (where a queen can't go), tap again to place a queen, and once more to clear it.
  5. There is always exactly one valid solution. Use logic, never guessing, to find it.

Full rules · Strategy library · Puzzle statistics

Questions about this puzzle

How hard is 9x9 Queens puzzle #166?

Puzzle #166 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and six of its regions are confined to a single row or column, which gives you a forced move early.

Does 9x9 puzzle #166 have only one solution?

Yes. Every puzzle in the 9x9 collection, including #166, has been verified to have exactly one valid arrangement of nine queens, and it can always be reached by logic alone — no guessing or backtracking needed.

Where should I place my first queen on puzzle #166?

Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.