12x12 Queens Puzzle #271
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 #271
What follows is a complete solve of puzzle #271, 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 region confined to one line.
Techniques this board needs: last square in a region, region confined to one line.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 12, column 4 is still open in rose, and since each colour must take a queen, that settles it. That clears row 12, column 4, the rest of the rose region and every square adjacent to it — diagonals included.
Step 2. The teal region is down to one open square, at row 11, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 11, the remaining teal squares, and the ring of neighbours around row 11, column 11.
Step 3. Mint cannot leave column 1 — every one of its open squares (3 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 8 squares in all.
Step 4. All of the red region's remaining squares (3 open squares) lie in column 2. 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 12 queens placed. Step 5. Khaki cannot leave column 12 — every one of its open squares (3 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 6 squares in all.
Step 6. The indigo region is down to one open square, at row 1, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 10, the remaining indigo squares, and the ring of neighbours around row 1, column 10.
Step 7. Blue cannot leave column 9 — every one of its open squares (3 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 6 squares in all.
The board after step 7 — 3 of 12 queens placed. Step 8. The sea green region is down to one open square, at row 10, column 8. Every colour holds exactly one queen, so that square is forced. Row 10 and column 8 are now spoken for, along with the squares touching that queen.
Step 9. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 7 squares in all.
Step 10. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: khaki has one square left, so its queen takes row 8, column 12; red has one square left, so its queen takes row 6, column 2; mint has one square left, so its queen takes row 4, column 1; slate has one square left, so its queen takes row 5, column 6; blue has one square left, so its queen takes row 3, column 9; pale yellow has one square left, so its queen takes row 7, column 7; orange has one square left, so its queen takes row 9, column 5; amber has one square left, so its queen takes row 2, 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 2, column 3.
The board after step 11 — 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 #271
12x12 puzzle #271 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.
There is exactly one way to finish #271, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these twelve regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #271 are: rose (1 square), teal (2 squares), mint (3 squares), red (4 squares), indigo (7 squares), pale yellow (8 squares), khaki (11 squares), sea green (14 squares), slate (15 squares), blue (17 squares), amber (31 squares), orange (31 squares). An even split would hand every color 12 squares, so the rose region is running 11 squares under that average while the orange region is the roomiest area on the grid with 31 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Rose has only 1 place to put its queen; orange has 31. The spread between them on this board is 30 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 3×1 box, and pale yellow the most diffuse at 40% of its 5×4 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 medium board.
Rose covers 1 square, spanning 1 row and 1 column (rows 12–12, columns 4–4). It never leaves row 12, so its queen is locked to that row.
Teal occupies 2 squares within rows 11–12, columns 11–11. It sits wholly inside column 11, so its queen must be in that column.
Mint: 3 squares across rows 4–6, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Red covers 4 squares, spanning 3 rows and 2 columns (rows 6–8, columns 1–2).
Indigo occupies 7 squares within rows 1–3, columns 10–12.
Pale yellow: 8 squares across rows 4–8, columns 6–9.
Khaki covers 11 squares, spanning 7 rows and 2 columns (rows 6–12, columns 11–12).
Sea green occupies 14 squares within rows 7–12, columns 7–10.
Slate: 15 squares across rows 4–9, columns 2–7.
Blue covers 17 squares, spanning 7 rows and 5 columns (rows 1–7, columns 8–12).
Amber occupies 31 squares within rows 1–5, columns 1–8.
Orange: 31 squares across rows 8–12, columns 1–9.
Where to start on this board
Begin where the choices are fewest. On this board that means rose, which owns just 1 square inside a 1×1 window running from row 12 to row 12 and column 4 to column 4. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because rose never leaves row 12, its queen must be in that row — and that instantly settles row 12 for everyone else. Sweep along it and X out every square that is not rose. 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 #271
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 10 are the narrowest, touched by only 3 colors. Columns 3, 5, 10 and 12 are the tightest columns, with 3 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 11 rows. By contrast row 8 meets 6 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 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 #271 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 #271 is rated medium
The medium label comes out of four measurable things about #271: 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 30. 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.
Stuck on #271 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 #271 the place to look for one is around row 1.
As a sanity check rather than a spoiler: the finished solution to #271 puts 4 queens on the outer border and 8 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 12x12 Queens puzzle #271?
Puzzle #271 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 12x12 puzzle #271 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #271, 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 #271?
Start with the rose region — the most constrained color on this board, with 1 square spanning rows 12–12 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.