9x9 Queens Puzzle #180
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 17-step reasoning is written out below.
Previous puzzle · All 9x9 puzzles · Next puzzle
Step-by-step solution for puzzle #180
What follows is a complete solve of puzzle #180, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 9 queen placements and 8 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 line confined to one region.
Techniques this board needs: last square in a region, region confined to one line, region shadow, line confined to one region, last square in a row.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 3, column 9 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 9, the rest of the blue region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (3 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 3. Orange cannot leave row 9 — every one of its open squares (2 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 8 squares in all.
Step 4. Wherever red ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
The board after step 4 — 1 of 9 queens placed. Step 5. Mint is down to 4 candidates in rows 4 and 5, columns 1–4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 6. The khaki region has 3 squares left, spread across rows 7 and 8, columns 5–7. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 7. Row 2 has only amber squares left (6 open squares). The row needs a queen and only amber can provide one, which pins that colour to this row and kills its squares elsewhere: 9 squares.
Step 8. Row 4 has a single open square left, at column 1 in the mint region. Every row needs a queen, so this one is forced. Cross out the whole of row 4 and column 1, the remaining mint squares, and the ring of neighbours around row 4, column 1.
Step 9. Only row 6, column 2 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 2, the rest of the red region and every square adjacent to it — diagonals included.
The board after step 9 — 3 of 9 queens placed. Step 10. Row 5 has a single open square left, at column 8 in the slate region. Every row needs a queen, so this one is forced. Row 5 and column 8 are now spoken for, along with the squares touching that queen.
Step 11. 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: 1 square in all.
Step 12. The pale yellow region has 2 squares left, spread across rows 7 and 8, columns 3 and 4. 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 13. 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: orange has one square left, so its queen takes row 9, column 5; khaki has one square left, so its queen takes row 8, column 7; indigo has one square left, so its queen takes row 1, column 6; pale yellow has one square left, so its queen takes row 7, column 4; amber has one square left, so its queen takes row 2, 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 2, column 3.
The board after step 13 — 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 #180
This is puzzle number 180 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 #180 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 #180 are: blue (1 square), orange (2 squares), mint (5 squares), indigo (6 squares), red (7 squares), pale yellow (9 squares), khaki (10 squares), slate (13 squares), amber (28 squares). An even split would hand every color 9 squares, so the blue region is running 8 squares under that average while the amber region is the roomiest area on the grid with 28 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Blue is working with 1 square while amber has 28 to spare, a gap of 27. 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. Blue is the tidiest shape on #180, packing 100% of its 1×1 bounding box, whereas slate straggles across its 6×4 box at just 54%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #180 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.
Blue: 1 square across rows 3–3, columns 9–9. It never leaves row 3, so its queen is locked to that row.
Orange covers 2 squares, spanning 1 row and 2 columns (rows 9–9, columns 4–5). It never leaves row 9, so its queen is locked to that row.
Mint occupies 5 squares within rows 4–5, columns 1–4.
Indigo: 6 squares across rows 1–2, columns 6–9.
Red covers 7 squares, spanning 4 rows and 3 columns (rows 6–9, columns 1–3).
Pale yellow occupies 9 squares within rows 6–8, columns 2–5.
Khaki: 10 squares across rows 7–9, columns 5–9.
Slate covers 13 squares, spanning 6 rows and 4 columns (rows 3–8, columns 6–9).
Amber occupies 28 squares within rows 1–7, columns 1–7.
Where to start on this board
Begin where the choices are fewest. On this board that means blue, which owns just 1 square inside a 1×1 window running from row 3 to row 3 and column 9 to column 9. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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, indigo and mint 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 #180
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 2 are the narrowest, touched by only 2 colors. Columns 1 and 8 are the tightest columns, with 3 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 7 meets 5 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 #180 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.
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 #180 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 #180 is rated easy
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 2 colors, and a region-size spread of 27. 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.
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 1 on this board.
As a sanity check rather than a spoiler: the finished solution to #180 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
- 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 #180?
Puzzle #180 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #180 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #180, 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 #180?
Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.