9x9 Queens Puzzle #8
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 13-step reasoning is written out below.
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Step-by-step solution for puzzle #8
What follows is a complete solve of puzzle #8, 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 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 (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: indigo has one square left, so its queen takes row 1, column 1; orange has one square left, so its queen takes row 9, column 9; khaki has one square left, so its queen takes row 8, column 7; pale yellow has one square left, so its queen takes row 7, 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 7, column 3.
Step 2. Amber cannot leave column 5 — 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: 7 squares in all.
Step 3. All of the blue region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.
The board after step 3 — 4 of 9 queens placed. Step 4. Wherever mint 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. Every open square left in column 4 (2 open squares) belongs to the slate region. Since that column must contain a queen, slate is the colour that supplies it — so slate squares anywhere else on the board are out, 1 square in all.
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: row 6 is down to one square, putting a queen on row 6, column 8; mint has one square left, so its queen takes row 4, column 6; amber has one square left, so its queen takes row 2, column 5; blue has one square left, so its queen takes row 3, column 2; 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.
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 #8
This is puzzle number 8 in the 9x9 collection, rated hard. 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 #8 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 #8 are: indigo (1 square), orange (1 square), amber (4 squares), pale yellow (10 squares), khaki (10 squares), red (12 squares), blue (14 squares), mint (14 squares), slate (15 squares). An even split would hand every color 9 squares, so the indigo region is running 8 squares under that average while the slate region is the roomiest area on the grid with 15 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Indigo is working with 1 square while slate has 15 to spare, a gap of 14. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and khaki the most diffuse at 42% of its 6×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a hard board.
Indigo occupies 1 square within rows 1–1, columns 1–1. It never leaves row 1, so its queen is locked to that row.
Orange: 1 square across rows 9–9, columns 9–9. It never leaves row 9, so its queen is locked to that row.
Amber covers 4 squares, spanning 3 rows and 2 columns (rows 1–3, columns 4–5).
Pale yellow occupies 10 squares within rows 7–9, columns 1–4.
Khaki: 10 squares across rows 4–9, columns 6–9.
Red covers 12 squares, spanning 6 rows and 4 columns (rows 4–9, columns 5–8).
Blue occupies 14 squares within rows 1–7, columns 1–3.
Mint: 14 squares across rows 1–4, columns 6–9.
Slate covers 15 squares, spanning 6 rows and 5 columns (rows 2–7, columns 2–6).
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 1 square inside a 1×1 window running from row 1 to row 1 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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 #8
A quick way to find the next move is to count how many different colors touch each line. On this board, row 8 is the narrowest, touched by only 3 colors. Columns 1, 2, 3, 4, 5, 7, 8 and 9 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 8 rows. Row 7 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
The middle of #8 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.
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 #8 is rated hard
The hard label comes out of four measurable things about #8: four of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 14. Boards that score tight on those measures give up their first queen fast.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a hard board from the rest.
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 8 on this board.
A non-spoiling distribution check: solved, #8 carries 2 queens on the perimeter against 7 queens inside, 2 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 #8?
Puzzle #8 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #8 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #8, 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 #8?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.