9x9 Queens Puzzle #274
Difficulty: hard. 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 12-step reasoning is written out below.
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Step-by-step solution for puzzle #274
What follows is a complete solve of puzzle #274, worked the way a person works it rather than the way a computer does. It runs to 12 deductions — 9 queen placements and 3 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 shadow.
Techniques this board needs: last square in a region, region confined to one line, region shadow, last square in a column.
Show the full walkthrough (5 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: mint has one square left, so its queen takes row 4, column 1; red has one square left, so its queen takes row 6, column 2; blue has one square left, so its queen takes row 3, column 3; slate has one square left, so its queen takes row 5, 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 5, column 4.
Step 2. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 4 squares in all.
Step 3. The khaki region has 4 squares left, spread across rows 7–9, columns 5 and 6. 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.
The board after step 3 — 4 of 9 queens placed. Step 4. Orange cannot leave column 7 — every one of its open squares (2 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 6 squares in all.
Step 5. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: amber has one square left, so its queen takes row 2, column 9; column 8 is down to one square, putting a queen on row 7, column 8; orange has one square left, so its queen takes row 9, column 7; khaki has one square left, so its queen takes row 8, column 5; indigo has one square left, so its queen takes row 1, 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 1, column 6.
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 #274
Board #274 of the 9x9 bank carries a hard 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, #274 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 #274 are: mint (1 square), orange (3 squares), amber (5 squares), blue (7 squares), red (7 squares), slate (11 squares), indigo (14 squares), khaki (14 squares), pale yellow (19 squares). An even split would hand every color 9 squares, so the mint region is running 8 squares under that average while the pale yellow region is the roomiest area on the grid with 19 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So mint, with 1 square, is under far more pressure than pale yellow with 19. A 18-square gap like this one rewards players who start where the choices are fewest.
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 pale yellow the most diffuse at 63% of its 6×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #274 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.
Orange occupies 3 squares within rows 8–9, columns 6–7.
Amber: 5 squares across rows 2–3, columns 7–9.
Blue covers 7 squares, spanning 3 rows and 3 columns (rows 1–3, columns 1–3).
Red occupies 7 squares within rows 4–8, columns 1–2.
Slate: 11 squares across rows 3–6, columns 3–6.
Indigo covers 14 squares, spanning 3 rows and 7 columns (rows 1–3, columns 3–9).
Khaki occupies 14 squares within rows 7–9, columns 1–6.
Pale yellow: 19 squares across rows 4–9, columns 5–9.
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 #274.
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. Amber 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 #274
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Columns 2, 4, 8 and 9 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 8 rows. Row 8, meeting 4 colors, is the opposite case — the busiest line on #274 and the last one you should expect to crack.
Working through the middle game
The middle of #274 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 #274 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 18. 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.
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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #274, start hunting for it near row 1.
Here is a shape check that gives nothing away: when #274 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.
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Questions about this puzzle
How hard is 9x9 Queens puzzle #274?
Puzzle #274 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #274 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #274, 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 #274?
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.