9x9 Queens Puzzle #12
Difficulty: medium. 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 12-step reasoning is written out below.
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Step-by-step solution for puzzle #12
What follows is a complete solve of puzzle #12, worked the way a person works it rather than the way a computer does. It runs to 12 deductions — 9 queen placements and 3 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 pairing argument on rows.
Techniques this board needs: last square in a region, region shadow, region confined to one line, pairing argument on rows.
Show the full walkthrough (7 steps) — contains the solution
Step 1. Only row 9, column 2 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 2, the rest of the orange region and every square adjacent to it — diagonals included.
Step 2. The khaki region is down to one open square, at row 8, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 6, the remaining khaki squares, and the ring of neighbours around row 8, column 6.
Step 3. The slate region has 3 squares left, spread across rows 5–7, columns 1 and 3. 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 4. All of the red region's remaining squares (2 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
The board after step 4 — 2 of 9 queens placed. Step 5. Only row 3, column 8 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 8, the rest of the blue region and every square adjacent to it — diagonals included.
Step 6. Here is the pairing argument. The red and pale yellow regions have no open squares outside rows 6 and 7 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 4 squares come off in one stroke.
Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: slate has one square left, so its queen takes row 5, column 3; mint has one square left, so its queen takes row 4, column 5; pale yellow has one square left, so its queen takes row 7, column 4; indigo has one square left, so its queen takes row 1, column 7; amber has one square left, so its queen takes row 2, column 1; red has one square left, so its queen takes row 6, column 9. 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 9.
The board after step 7 — 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 #12
This is puzzle number 12 in the 9x9 collection, rated medium. 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.
Like every board on this site, #12 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #12 are: orange (1 square), khaki (2 squares), red (4 squares), blue (6 squares), slate (8 squares), amber (10 squares), indigo (11 squares), pale yellow (14 squares), mint (25 squares). An even split would hand every color 9 squares, so the orange region is running 8 squares under that average while the mint region is the roomiest area on the grid with 25 squares.
Every color takes one queen and one only, whatever its size — which is why the 24 square difference between orange and mint is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Square count is only half the story — how a color is arranged counts too. Red is the tidiest shape on #12, packing 100% of its 4×1 bounding box, whereas slate straggles across its 5×3 box at just 53%. 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.
Orange: 1 square across rows 9–9, columns 2–2. It never leaves row 9, so its queen is locked to that row.
Khaki covers 2 squares, spanning 2 rows and 1 column (rows 8–9, columns 6–6). It sits wholly inside column 6, so its queen must be in that column.
Red occupies 4 squares within rows 6–9, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.
Blue: 6 squares across rows 1–5, columns 8–9.
Slate covers 8 squares, spanning 5 rows and 3 columns (rows 5–9, columns 1–3).
Amber occupies 10 squares within rows 1–5, columns 1–3.
Indigo: 11 squares across rows 1–2, columns 3–8.
Pale yellow covers 14 squares, spanning 4 rows and 5 columns (rows 6–9, columns 2–6).
Mint occupies 25 squares within rows 3–9, columns 3–8.
Where to start on this board
Begin where the choices are fewest. On this board that means orange, which owns just 1 square inside a 1×1 window running from row 9 to row 9 and column 2 to column 2. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. 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 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 #12
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 and 4 are the narrowest, touched by only 3 colors. Columns 1, 7 and 9 are the tightest columns, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 8 rows. Row 9, meeting 6 colors, is the opposite case — the busiest line on #12 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.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #12 is rated medium
Ratings track how generous the opening is. On #12 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 24-square gap between the largest and smallest regions. Those four numbers largely explain the medium 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.
If #12 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #12 is column 1.
Here is a shape check that gives nothing away: when #12 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.
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Questions about this puzzle
How hard is 9x9 Queens puzzle #12?
Puzzle #12 is rated medium. 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 #12 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #12, 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 #12?
Start with the orange region — the most constrained color on this board, with 1 square spanning rows 9–9 and columns 2–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.