9x9 Queens Puzzle #186
Difficulty: medium. 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 15-step reasoning is written out below.
Previous puzzle · All 9x9 puzzles · Next puzzle
Step-by-step solution for puzzle #186
What follows is a complete solve of puzzle #186, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 9 queen placements and 6 elimination steps 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 pairing argument on columns.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Only row 5, column 9 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 9, the rest of the slate region and every square adjacent to it — diagonals included.
Step 2. The indigo region is down to one open square, at row 1, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 8, the remaining indigo squares, and the ring of neighbours around row 1, column 8.
Step 3. Amber cannot leave column 4 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 9 squares in all.
The board after step 3 — 2 of 9 queens placed. Step 4. Wherever mint ends up among its 2 squares, the same squares fall within reach of it — 4 squares in total, impossible regardless of how the colour resolves.
Step 5. Only row 2, column 4 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 4, the rest of the amber region and every square adjacent to it — diagonals included.
Step 6. The red region has 4 squares left, spread across rows 6–8, columns 2 and 3. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 7. Wherever orange 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.
The board after step 7 — 3 of 9 queens placed. Step 8. Here is the pairing argument. The red, pale yellow, khaki, and orange regions have no open squares outside rows 6–9 — 4 colours confined to 4 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 3 squares come off in one stroke.
Step 9. Mint and pale yellow are now boxed into columns 5 and 7 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 3 squares at once.
Step 10. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: orange has one square left, so its queen takes row 9, column 6; khaki has one square left, so its queen takes row 8, column 3; red has one square left, so its queen takes row 6, column 2; pale yellow has one square left, so its queen takes row 7, column 7; mint has one square left, so its queen takes row 4, column 5; blue has one square left, so its queen takes row 3, column 1. 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 3, column 1.
The board after step 10 — 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 #186
Board #186 of the 9x9 bank carries a medium 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.
Puzzle #186 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #186 are: slate (1 square), amber (3 squares), orange (3 squares), red (5 squares), indigo (6 squares), mint (11 squares), khaki (11 squares), blue (18 squares), pale yellow (23 squares). An even split would hand every color 9 squares, so the slate region is running 8 squares under that average while the pale yellow region is the roomiest area on the grid with 23 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Slate has only 1 place to put its queen; pale yellow has 23. The spread between them on this board is 22 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 amber is the most solid, filling 100% of its 3×1 box, and khaki the most diffuse at 46% of its 4×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #186 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.
Slate: 1 square across rows 5–5, columns 9–9. It never leaves row 5, so its queen is locked to that row.
Amber covers 3 squares, spanning 3 rows and 1 column (rows 1–3, columns 4–4). It sits wholly inside column 4, so its queen must be in that column.
Orange occupies 3 squares within rows 8–9, columns 5–6.
Red: 5 squares across rows 6–8, columns 2–4.
Indigo covers 6 squares, spanning 4 rows and 2 columns (rows 1–4, columns 8–9).
Mint occupies 11 squares within rows 1–4, columns 4–8.
Khaki: 11 squares across rows 6–9, columns 1–6.
Blue covers 18 squares, spanning 8 rows and 3 columns (rows 1–8, columns 1–3).
Pale yellow occupies 23 squares within rows 2–9, columns 4–9.
Where to start on this board
Open on the tightest color. Here that is slate, confined to 1 square between rows 5 and 5 and columns 9 and 9. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #186.
Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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. Orange is no more than two rows tall, so its queen is 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 #186
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5 and 9 are the narrowest, touched by only 3 colors. Columns 1 and 7 are the tightest columns, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 8 rows. Row 8, meeting 5 colors, is the opposite case — the busiest line on #186 and the last one you should expect to crack.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
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.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #186 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 22. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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 #186 the place to look for one is around column 1.
Here is a shape check that gives nothing away: when #186 is solved, 4 queens sit on the outer edge of the grid and 5 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
How to play Queens
- The board is an N×N grid divided into N colored regions.
- Place exactly one queen (♛) in each row, each column, and each colored region.
- No two queens may touch each other — not horizontally, vertically, or diagonally.
- 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.
- 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 #186?
Puzzle #186 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #186 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #186, 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 #186?
Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.