12x12 Queens Puzzle #291
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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #291
What follows is a complete solve of puzzle #291, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 12 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 line confined to one region.
Techniques this board needs: last square in a region, region shadow, line confined to one region, last square in a column.
Show the full walkthrough (6 steps) — contains the solution
Step 1. Only row 1, column 8 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 8, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The khaki region is down to one open square, at row 8, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 1, the remaining khaki squares, and the ring of neighbours around row 8, column 1.
Step 3. The amber region has 3 squares left, spread across rows 2 and 3, columns 9–11. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
The board after step 3 — 2 of 12 queens placed. Step 4. Wherever blue ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Column 12 has only pale yellow squares left (10 open squares). The column needs a queen and only pale yellow can provide one, which pins that colour to this column and kills its squares elsewhere: 20 squares.
Step 6. From here the board cascades. Keep alternating the region sweep and the line sweep and 10 queens fall out in order without any new idea being needed: column 11 is down to one square, putting a queen on row 2, column 11; blue has one square left, so its queen takes row 3, column 7; column 10 is down to one square, putting a queen on row 12, column 10; teal has one square left, so its queen takes row 11, column 3; orange has one square left, so its queen takes row 9, column 4; sea green has one square left, so its queen takes row 10, column 6; column 9 is down to one square, putting a queen on row 6, column 9; slate has one square left, so its queen takes row 5, column 2; 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 12. 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 12.
The board after step 6 — 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 #291
12x12 puzzle #291 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, #291 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 #291 are: indigo (1 square), khaki (1 square), rose (6 squares), amber (8 squares), teal (10 squares), blue (11 squares), orange (11 squares), sea green (12 squares), slate (14 squares), red (15 squares), mint (20 squares), pale yellow (35 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the pale yellow region is the roomiest area on the grid with 35 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Indigo is working with 1 square while pale yellow has 35 to spare, a gap of 34. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and rose the most diffuse at 50% of its 3×4 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.
Indigo: 1 square across rows 1–1, columns 8–8. It never leaves row 1, so its queen is locked to that row.
Khaki covers 1 square, spanning 1 row and 1 column (rows 8–8, columns 1–1). It never leaves row 8, so its queen is locked to that row.
Rose occupies 6 squares within rows 10–12, columns 7–10.
Amber: 8 squares across rows 1–3, columns 9–12.
Teal covers 10 squares, spanning 4 rows and 5 columns (rows 9–12, columns 1–5).
Blue occupies 11 squares within rows 1–3, columns 4–8.
Orange: 11 squares across rows 8–11, columns 2–5.
Sea green covers 12 squares, spanning 5 rows and 4 columns (rows 8–12, columns 5–8).
Slate occupies 14 squares within rows 2–7, columns 1–4.
Red: 15 squares across rows 4–8, columns 5–10.
Mint covers 20 squares, spanning 6 rows and 6 columns (rows 1–6, columns 1–6).
Pale yellow occupies 35 squares within rows 2–12, columns 7–12.
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 1 square inside a 1×1 window running from row 1 to row 1 and column 8 to column 8. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Khaki 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 #291
A quick way to find the next move is to count how many different colors touch each line. On this board, row 7 is the narrowest, touched by only 3 colors. Columns 11 and 12 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 11 rows. By contrast row 11 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
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 #291 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 #291 is rated medium
Ratings track how generous the opening is. On #291 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 34-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
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.
If #291 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.
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 11 on this board.
As a sanity check rather than a spoiler: the finished solution to #291 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 #291?
Puzzle #291 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 #291 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #291, 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 #291?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.