12x12 Queens Puzzle #231
Difficulty: medium. Place 12 queens on this 12x12 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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #231
What follows is a complete solve of puzzle #231, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 12 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 pairing argument on rows.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows, last square in a column, last square in a row.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Only row 4, column 7 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 7, the rest of the mint region and every square adjacent to it — diagonals included.
Step 2. All of the orange region's remaining squares (4 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 3. Red cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 10 squares in all.
The board after step 3 — 1 of 12 queens placed. Step 4. The rose region is down to one open square, at row 12, column 3. Every colour holds exactly one queen, so that square is forced. Row 12 and column 3 are now spoken for, along with the squares touching that queen.
Step 5. Only row 11, column 12 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 12, the rest of the teal region and every square adjacent to it — diagonals included.
Step 6. The sea green region has 3 squares left, spread across rows 9 and 10, columns 4 and 5. 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 7. Orange and sea green are now boxed into rows 9 and 10 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 9 squares at once.
The board after step 7 — 3 of 12 queens placed. Step 8. Khaki is down to 5 candidates in rows 5–8, columns 10 and 11, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about khaki itself.
Step 9. Slate, red, pale yellow, and khaki are now boxed into rows 5–8 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 7 squares at once.
Step 10. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 10; column 9 is down to one square, putting a queen on row 1, column 9; column 8 is down to one square, putting a queen on row 7, column 8; row 5 is down to one square, putting a queen on row 5, column 4; sea green has one square left, so its queen takes row 10, column 5; amber has one square left, so its queen takes row 2, column 6; orange has one square left, so its queen takes row 9, column 1; red has one square left, so its queen takes row 6, column 2; khaki has one square left, so its queen takes row 8, column 11. 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 8, column 11.
The board after step 10 — 12 of 12 queens placed.
That completes the board: 12 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 12x12 Queens puzzle #231
12x12 puzzle #231 is rated medium. Twelve colored regions cover its 144 squares, and your job is to seat twelve queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Like every board on this site, #231 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 #231 are: mint (1 square), orange (4 squares), teal (4 squares), rose (5 squares), red (7 squares), sea green (13 squares), indigo (15 squares), amber (15 squares), blue (15 squares), slate (18 squares), khaki (22 squares), pale yellow (25 squares). An even split would hand every color 12 squares, so the mint region is running 11 squares under that average while the pale yellow region is the roomiest area on the grid with 25 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Mint has only 1 place to put its queen; pale yellow has 25. The spread between them on this board is 24 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here mint is the most solid, filling 100% of its 1×1 box, and slate the most diffuse at 45% of its 8×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
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.
Mint: 1 square across rows 4–4, columns 7–7. It never leaves row 4, so its queen is locked to that row.
Orange covers 4 squares, spanning 4 rows and 1 column (rows 9–12, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Teal occupies 4 squares within rows 11–12, columns 10–12.
Rose: 5 squares across rows 9–12, columns 2–3.
Red covers 7 squares, spanning 5 rows and 2 columns (rows 4–8, columns 1–2).
Sea green occupies 13 squares within rows 9–12, columns 3–7.
Indigo: 15 squares across rows 1–3, columns 7–12.
Amber covers 15 squares, spanning 3 rows and 6 columns (rows 1–3, columns 2–7).
Blue occupies 15 squares within rows 3–8, columns 8–12.
Slate: 18 squares across rows 1–8, columns 1–5.
Khaki covers 22 squares, spanning 8 rows and 5 columns (rows 5–12, columns 8–12).
Pale yellow occupies 25 squares within rows 4–11, columns 4–8.
Where to start on this board
Begin where the choices are fewest. On this board that means mint, which owns just 1 square inside a 1×1 window running from row 4 to row 4 and column 7 to column 7. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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. Teal 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 #231
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 3 colors. Columns 1, 6 and 9 are the tightest columns, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 11 rows. Row 11 sits at the far end with 6 colors crossing it; it will almost certainly be among the last to settle.
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.
With twelve queens to seat and twelve regions competing over 144 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 12x12 boards quickly and players who stall halfway.
Resist the plausible-looking queen. On #231 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 #231 is rated medium
Ratings track how generous the opening is. On #231 you get three 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.
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.
If #231 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 12x12
At 12x12 you are managing 144 squares, and holding the whole board in your head will not work. Split it into quadrants and solve locally. Most useful deductions on a grid this large are regional — a color pinched between two placed queens, or a band of rows that two regions must share. Trust the marks on the board over your memory.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #231 the place to look for one is around row 1.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 8 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 12x12 Queens puzzle #231?
Puzzle #231 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #231 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #231, has been verified to have exactly one valid arrangement of twelve queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #231?
Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.