9x9 Queens Puzzle #276
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 13-step reasoning is written out below.
Previous puzzle · All 9x9 puzzles · Next puzzle
Step-by-step solution for puzzle #276
What follows is a complete solve of puzzle #276, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 9 queen placements and 4 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.
Show the full walkthrough (6 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: amber has one square left, so its queen takes row 2, column 8; mint has one square left, so its queen takes row 4, column 9; red has one square left, so its queen takes row 6, column 1; slate has one square left, so its queen takes row 5, column 3. 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 3.
Step 2. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 2 squares in all.
Step 3. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
The board after step 3 — 4 of 9 queens placed. Step 4. Wherever pale yellow 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.
Step 5. All of the khaki region's remaining squares (2 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 6. 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: pale yellow has one square left, so its queen takes row 7, column 4; blue has one square left, so its queen takes row 3, column 2; orange has one square left, so its queen takes row 9, column 5; indigo has one square left, so its queen takes row 1, column 6; khaki has one square left, so its queen takes row 8, 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 8, column 7.
The board after step 6 — 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 #276
This is puzzle number 276 in the 9x9 collection, rated easy. The grid holds 81 squares split between nine colored regions, and a finished board carries nine queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
Puzzle #276 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 #276 are: amber (1 square), red (1 square), slate (4 squares), indigo (7 squares), mint (7 squares), pale yellow (10 squares), orange (12 squares), khaki (18 squares), blue (21 squares). An even split would hand every color 9 squares, so the amber region is running 8 squares under that average while the blue region is the roomiest area on the grid with 21 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Amber is working with 1 square while blue has 21 to spare, a gap of 20. 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. Amber is the tidiest shape on #276, packing 100% of its 1×1 bounding box, whereas orange straggles across its 3×8 box at just 50%. 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.
Amber: 1 square across rows 2–2, columns 8–8. It never leaves row 2, so its queen is locked to that row.
Red covers 1 square, spanning 1 row and 1 column (rows 6–6, columns 1–1). It never leaves row 6, so its queen is locked to that row.
Slate occupies 4 squares within rows 5–7, columns 2–3.
Indigo: 7 squares across rows 1–3, columns 5–8.
Mint covers 7 squares, spanning 5 rows and 2 columns (rows 1–5, columns 8–9).
Pale yellow occupies 10 squares within rows 6–9, columns 1–5.
Orange: 12 squares across rows 7–9, columns 2–9.
Khaki covers 18 squares, spanning 6 rows and 5 columns (rows 3–8, columns 5–9).
Blue occupies 21 squares within rows 1–5, columns 1–5.
Where to start on this board
Begin where the choices are fewest. On this board that means amber, which owns just 1 square inside a 1×1 window running from row 2 to row 2 and column 8 to column 8. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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. Red 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 #276
A quick way to find the next move is to count how many different colors touch each line. On this board, row 9 is the narrowest, touched by only 2 colors. Columns 1, 4, 6, 7 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 7, meeting 4 colors, is the opposite case — the busiest line on #276 and the last one you should expect to crack.
Working through the middle game
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
Two checks, run alternately, will carry you through the 81 squares of this grid. First: has any of the nine regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 9x9 boards almost always run one of those checks and forget the other.
Resist the plausible-looking queen. On #276 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #276 is rated easy
Ratings track how generous the opening is. On #276 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 20-square gap between the largest and smallest regions. Those four numbers largely explain the easy 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 9 on this board.
Here is a shape check that gives nothing away: when #276 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 #276?
Puzzle #276 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #276 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #276, 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 #276?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.