8x8 Queens Puzzle #267
Difficulty: easy. Place 8 queens on this 8x8 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 9-step reasoning is written out below.
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Step-by-step solution for puzzle #267
What follows is a complete solve of puzzle #267, worked the way a person works it rather than the way a computer does. It runs to 9 deductions — 8 queen placements and 1 elimination step 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 shadow.
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: slate has one square left, so its queen takes row 5, column 3; indigo has one square left, so its queen takes row 1, column 4; red has one square left, so its queen takes row 6, column 7; khaki has one square left, so its queen takes row 8, column 8; pale yellow has one square left, so its queen takes row 7, column 5. 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 5.
Step 2. The amber region has 3 squares left, spread across rows 2 and 3, columns 1 and 2. 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 3. Only row 4, column 1 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 1, in mint and in the ring around that square is now dead.
The board after step 3 — 6 of 8 queens placed. Step 4. The amber region is down to one open square, at row 2, column 2. Every colour holds exactly one queen, so that square is forced. Row 2 and column 2 are now spoken for, along with the squares touching that queen.
Step 5. Only row 3, column 6 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 6, the rest of the blue region and every square adjacent to it — diagonals included.
The board after step 5 — 8 of 8 queens placed.
That completes the board: 8 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 8x8 Queens puzzle #267
8x8 puzzle #267 is rated easy. Eight colored regions cover its 64 squares, and your job is to seat eight queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Puzzle #267 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 #267 are: slate (1 square), red (1 square), indigo (2 squares), khaki (4 squares), amber (8 squares), mint (9 squares), blue (16 squares), pale yellow (23 squares). An even split would hand every color 8 squares, so the slate region is running 7 squares under that average while the pale yellow region is the roomiest area on the grid with 23 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 pale yellow has 23 to spare, a gap of 22. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×2 box that encloses it, while pale yellow is the most scattered at 55% of its 6×7 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
Region by region
Below is every color on #267 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.
Slate: 1 square across rows 5–5, columns 3–3. It never leaves row 5, so its queen is locked to that row.
Red covers 1 square, spanning 1 row and 1 column (rows 6–6, columns 7–7). It never leaves row 6, so its queen is locked to that row.
Indigo occupies 2 squares within rows 1–1, columns 3–4. It never leaves row 1, so its queen is locked to that row.
Khaki: 4 squares across rows 7–8, columns 7–8.
Amber covers 8 squares, spanning 4 rows and 3 columns (rows 1–4, columns 1–3).
Mint occupies 9 squares within rows 3–8, columns 1–2.
Blue: 16 squares across rows 1–4, columns 4–8.
Pale yellow covers 23 squares, spanning 6 rows and 7 columns (rows 3–8, columns 2–8).
Where to start on this board
Begin where the choices are fewest. On this board that means slate, which owns just 1 square inside a 1×1 window running from row 5 to row 5 and column 3 to column 3. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
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, red and khaki 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 #267
A quick way to find the next move is to count how many different colors touch each line. On this board, row 2 is the narrowest, touched by only 2 colors. Columns 1, 5 and 6 are the tightest columns, with 2 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 7 rows. By contrast row 4 meets 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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 eight 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 8x8 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 #267 is rated easy
What earns a board its rating is the shape of its opening. Here that opening offers five single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 22. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
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 8x8
At 8x8 the whole grid stays within a single glance, which makes systematic scanning practical. Read the rows in order and count the colors in each — a row touched by two colors is far more constrained than one touched by five, and that is usually where the next forced move hides. The board is small enough that re-scanning from the top after each placement costs almost nothing.
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 2 on this board.
As a sanity check rather than a spoiler: the finished solution to #267 puts 3 queens on the outer border and 5 queens in the interior, 1 of them in an actual 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.
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Questions about this puzzle
How hard is 8x8 Queens puzzle #267?
Puzzle #267 is rated easy. 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 8x8 puzzle #267 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #267, has been verified to have exactly one valid arrangement of eight queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #267?
Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.