9x9 Queens Puzzle #227
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 11-step reasoning is written out below.
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Step-by-step solution for puzzle #227
What follows is a complete solve of puzzle #227, worked the way a person works it rather than the way a computer does. It runs to 11 deductions — 9 queen placements and 2 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 region confined to one line.
Techniques this board needs: last square in a region, region confined to one line.
Show the full walkthrough (4 steps) — contains the solution
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: slate has one square left, so its queen takes row 5, column 2; indigo has one square left, so its queen takes row 1, column 1; khaki has one square left, so its queen takes row 8, column 9; amber has one square left, so its queen takes row 2, column 7; orange has one square left, so its queen takes row 9, column 6. 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 9, column 6.
Step 2. All of the mint region's remaining squares (2 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
The board after step 2 — 5 of 9 queens placed. Step 3. Pale yellow cannot leave column 4 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 1 square in all.
Step 4. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 3; mint has one square left, so its queen takes row 4, column 5; red has one square left, so its queen takes row 6, column 8; pale yellow has one square left, so its queen takes row 7, column 4. 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 7, column 4.
The board after step 4 — 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 #227
9x9 puzzle #227 is rated medium. Nine colored regions cover its 81 squares, and your job is to seat nine queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Puzzle #227 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 #227 are: slate (1 square), khaki (1 square), indigo (2 squares), amber (5 squares), red (9 squares), orange (11 squares), pale yellow (13 squares), mint (17 squares), blue (22 squares). An even split would hand every color 9 squares, so the slate region is running 8 squares under that average while the blue region is the roomiest area on the grid with 22 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Slate is working with 1 square while blue has 22 to spare, a gap of 21. Attack the cramped end and the roomy regions tend to resolve themselves.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #227, packing 100% of its 1×2 bounding box, whereas pale yellow straggles across its 4×6 box at just 54%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Slate occupies 1 square within rows 5–5, columns 2–2. It never leaves row 5, so its queen is locked to that row.
Khaki: 1 square across rows 8–8, columns 9–9. It never leaves row 8, so its queen is locked to that row.
Indigo covers 2 squares, spanning 1 row and 2 columns (rows 1–1, columns 1–2). It never leaves row 1, so its queen is locked to that row.
Amber occupies 5 squares within rows 1–2, columns 7–9.
Red: 9 squares across rows 4–6, columns 6–9.
Orange covers 11 squares, spanning 3 rows and 5 columns (rows 7–9, columns 5–9).
Pale yellow occupies 13 squares within rows 6–9, columns 1–6.
Mint: 17 squares across rows 1–5, columns 4–9.
Blue covers 22 squares, spanning 8 rows and 4 columns (rows 1–8, columns 1–4).
Where to start on this board
Slate is the natural opening on #227: it is the smallest region on the grid at 1 square, boxed into rows 5–5 and columns 2–2. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
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. Indigo, khaki and amber 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 #227
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3 and 9 are the narrowest, touched by only 2 colors. Column 3 is the tightest column, with 2 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 8 rows. Row 8 is the crowded extreme at 4 colors — worth revisiting later, not now.
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.
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 #227 is rated medium
Ratings track how generous the opening is. On #227 you get five regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 21-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 3 on this board.
A non-spoiling distribution check: solved, #227 carries 3 queens on the perimeter against 6 queens inside, 1 of them cornered. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
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.
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Questions about this puzzle
How hard is 9x9 Queens puzzle #227?
Puzzle #227 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #227 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #227, 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 #227?
Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 2–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.