12x12 Queens Puzzle #287
Difficulty: easy. 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 24-step reasoning is written out below.
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Step-by-step solution for puzzle #287
What follows is a complete solve of puzzle #287, worked the way a person works it rather than the way a computer does. It runs to 24 deductions — 12 queen placements and 12 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 columns.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows, pairing argument on columns, last square in a column.
Show the full walkthrough (16 steps) — contains the solution
Step 1. Only row 7, column 6 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 6, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 2. The khaki region is down to one open square, at row 8, column 12. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 12, the remaining khaki squares, and the ring of neighbours around row 8, column 12.
Step 3. Only row 11, column 1 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 1, in teal and in the ring around that square is now dead.
Step 4. 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: 9 squares come off.
Step 5. Amber is down to 6 candidates in rows 2–5, columns 3–5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
The board after step 5 — 3 of 12 queens placed. Step 6. The sea green region has 5 squares left, spread across rows 10 and 12, columns 5, 7, 8, 9, and 10. 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. Sea green and rose are now boxed into rows 10 and 12 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 7 squares at once.
Step 8. 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: 6 squares come off.
Step 9. Indigo and rose are now boxed into columns 10 and 11 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 9 squares at once.
Step 10. Wherever slate ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 11. Blue, slate, orange, and sea green are now boxed into columns 5, 7, 8, and 9 and nothing else. That is 4 colours needing 4 columns, so they fill those columns between them — which locks every remaining colour out and removes 6 squares at once.
The board after step 11 — 3 of 12 queens placed. Step 12. The amber region has 3 squares left, spread across rows 2 and 3, columns 3 and 4. 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 13. Wherever red ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 14. Here is the pairing argument. The slate and red regions have no open squares outside rows 5 and 6 — 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: 1 square come off in one stroke.
Step 15. The mint region has 4 squares left, spread across rows 2–4, columns 2 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 16. 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: column 3 is down to one square, putting a queen on row 4, column 3; amber has one square left, so its queen takes row 2, column 4; red has one square left, so its queen takes row 6, column 2; slate has one square left, so its queen takes row 5, column 9; blue has one square left, so its queen takes row 3, column 8; orange has one square left, so its queen takes row 9, column 7; sea green has one square left, so its queen takes row 10, column 5; rose has one square left, so its queen takes row 12, column 11; indigo has one square left, so its queen takes row 1, column 10. 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 1, column 10.
The board after step 16 — 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 #287
12x12 puzzle #287 is rated easy. 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, #287 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 #287 are: pale yellow (1 square), teal (1 square), khaki (2 squares), orange (6 squares), indigo (8 squares), amber (9 squares), sea green (12 squares), rose (12 squares), mint (13 squares), blue (18 squares), slate (22 squares), red (40 squares). An even split would hand every color 12 squares, so the pale yellow region is running 11 squares under that average while the red region is the roomiest area on the grid with 40 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Pale yellow has only 1 place to put its queen; red has 40. The spread between them on this board is 39 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 pale yellow is the most solid, filling 100% of its 1×1 box, and indigo the most diffuse at 44% of its 6×3 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 easy board.
Pale yellow occupies 1 square within rows 7–7, columns 6–6. It never leaves row 7, so its queen is locked to that row.
Teal: 1 square across rows 11–11, columns 1–1. It never leaves row 11, so its queen is locked to that row.
Khaki covers 2 squares, spanning 2 rows and 1 column (rows 7–8, columns 12–12). It sits wholly inside column 12, so its queen must be in that column.
Orange occupies 6 squares within rows 9–10, columns 6–9.
Indigo: 8 squares across rows 1–6, columns 10–12.
Amber covers 9 squares, spanning 5 rows and 4 columns (rows 1–5, columns 2–5).
Sea green occupies 12 squares within rows 10–12, columns 3–10.
Rose: 12 squares across rows 9–12, columns 8–12.
Mint covers 13 squares, spanning 6 rows and 3 columns (rows 1–6, columns 1–3).
Blue occupies 18 squares within rows 1–5, columns 5–10.
Slate: 22 squares across rows 2–9, columns 7–11.
Red covers 40 squares, spanning 10 rows and 7 columns (rows 3–12, columns 1–7).
Where to start on this board
Begin where the choices are fewest. On this board that means pale yellow, which owns just 1 square inside a 1×1 window running from row 7 to row 7 and column 6 to column 6. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because pale yellow never leaves row 7, its queen must be in that row — and that instantly settles row 7 for everyone else. Sweep along it and X out every square that is not pale yellow. 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, khaki and orange 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 #287
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 8 and 12 are the narrowest, touched by only 3 colors. Columns 1, 2, 4, 11 and 12 are the tightest columns, with 3 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 11 rows. Row 5, meeting 6 colors, is the opposite case — the busiest line on #287 and the last one you should expect to crack.
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 #287 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 #287 is rated easy
The easy label comes out of four measurable things about #287: 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 39. Boards that score tight on those measures give up their first queen fast.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a easy board from the rest.
If #287 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 #287 the place to look for one is around row 8.
Here is a shape check that gives nothing away: when #287 is solved, 4 queens sit on the outer edge of the grid and 8 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 12x12 Queens puzzle #287?
Puzzle #287 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 12x12 puzzle #287 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #287, 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 #287?
Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.