9x9 Queens Puzzle #127
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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #127
What follows is a complete solve of puzzle #127, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 9 queen placements and 6 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 proof by contradiction.
Techniques this board needs: last square in a region, region confined to one line, pairing argument on rows, proof by contradiction.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 8, column 5 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 5, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.
Step 3. Only row 3, column 9 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 9, in blue and in the ring around that square is now dead.
Step 4. The indigo region is down to one open square, at row 1, column 8. Every colour holds exactly one queen, so that square is forced. Row 1 and column 8 are now spoken for, along with the squares touching that queen.
The board after step 4 — 3 of 9 queens placed. Step 5. Only row 9, column 7 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 7, the rest of the orange region and every square adjacent to it — diagonals included.
Step 6. All of the red region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 7. Pale yellow cannot leave column 3 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 4 squares in all.
The board after step 7 — 4 of 9 queens placed. Step 8. All of the amber 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.
Step 9. Red and pale yellow are now boxed into rows 6 and 7 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 1 square at once.
Step 10. Now a short proof by contradiction. Suppose the amber queen went to row 5, column 2. Follow the forced moves that would create and row 6 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 11. 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 2; mint has one square left, so its queen takes row 4, column 6; slate has one square left, so its queen takes row 5, column 4; pale yellow has one square left, so its queen takes row 7, column 3; red has one square left, so its queen takes row 6, column 1. 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 6, column 1.
The board after step 11 — 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 #127
9x9 puzzle #127 is rated easy. Nine colored regions cover its 81 squares, and your job is to seat nine queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Puzzle #127 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 #127 are: khaki (1 square), indigo (2 squares), blue (2 squares), red (4 squares), orange (9 squares), amber (12 squares), pale yellow (13 squares), slate (15 squares), mint (23 squares). An even split would hand every color 9 squares, so the khaki region is running 8 squares under that average while the mint 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. Khaki is working with 1 square while mint 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 slate is the most scattered at 42% of its 6×6 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
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 easy board.
Khaki covers 1 square, spanning 1 row and 1 column (rows 8–8, columns 5–5). It never leaves row 8, so its queen is locked to that row.
Indigo occupies 2 squares within rows 1–1, columns 8–9. It never leaves row 1, so its queen is locked to that row.
Blue: 2 squares across rows 2–3, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.
Red covers 4 squares, spanning 4 rows and 1 column (rows 6–9, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Orange occupies 9 squares within rows 6–9, columns 7–9.
Amber: 12 squares across rows 1–5, columns 1–3.
Pale yellow covers 13 squares, spanning 4 rows and 4 columns (rows 6–9, columns 2–5).
Slate occupies 15 squares within rows 4–9, columns 2–7.
Mint: 23 squares across rows 1–6, columns 4–9.
Where to start on this board
Khaki is the natural opening on #127: it is the smallest region on the grid at 1 square, boxed into rows 8–8 and columns 5–5. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because khaki never leaves row 8, its queen must be in that row — and that instantly settles row 8 for everyone else. Sweep along it and X out every square that is not khaki. 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 and blue 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 #127
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 4 and 5 are the narrowest, touched by only 3 colors. Columns 1 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 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 8 rows. By contrast row 8 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
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
With nine queens to seat and nine regions competing over 81 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 9x9 boards quickly and players who stall halfway.
Resist the plausible-looking queen. On #127 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 #127 is rated easy
The easy label comes out of four measurable things about #127: five 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 22. Boards that score tight on those measures give up their first queen fast.
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 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 column 1 on this board.
As a sanity check rather than a spoiler: the finished solution to #127 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.
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Questions about this puzzle
How hard is 9x9 Queens puzzle #127?
Puzzle #127 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #127 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #127, 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 #127?
Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.