12x12 Queens Puzzle #285
Difficulty: hard. 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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #285
What follows is a complete solve of puzzle #285, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 12 queen placements and 9 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, line confined to one region, last square in a column, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 1, column 7 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 7, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The rose region is down to one open square, at row 12, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 12 and column 8, the remaining rose squares, and the ring of neighbours around row 12, column 8.
Step 3. Amber cannot leave row 2 — every one of its open squares (3 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 7 squares in all.
Step 4. Wherever mint 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 5. Slate is down to 4 candidates in rows 3–5, columns 5 and 6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
The board after step 5 — 2 of 12 queens placed. Step 6. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 12 squares come off.
Step 7. Wherever sea green 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 8. Every open square left in column 12 (8 open squares) belongs to the orange region. Since that column must contain a queen, orange is the colour that supplies it — so orange squares anywhere else on the board are out, 13 squares in all.
Step 9. Scan column 11 and only row 2, column 11 remains — a amber square. Every column takes a queen, so it takes this one. Row 2 and column 11 are now spoken for, along with the squares touching that queen.
The board after step 9 — 3 of 12 queens placed. Step 10. Here is the pairing argument. The blue and mint regions have no open squares outside rows 3 and 4 — 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: 6 squares come off in one stroke.
Step 11. Only row 5, column 6 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 6, in slate and in the ring around that square is now dead.
Step 12. All of the red region's remaining squares (2 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
Step 13. Blue, red, pale yellow, and sea green are now boxed into columns 1–4 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 9 squares at once.
Step 14. 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: teal has one square left, so its queen takes row 11, column 5; sea green has one square left, so its queen takes row 10, column 1; pale yellow has one square left, so its queen takes row 7, column 2; red has one square left, so its queen takes row 6, column 4; blue has one square left, so its queen takes row 3, column 3; khaki has one square left, so its queen takes row 8, column 9; mint has one square left, so its queen takes row 4, column 10; orange has one square left, so its queen takes row 9, 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 9, column 12.
The board after step 14 — 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 #285
Puzzle #285 is one of the hard-rated boards in the 12x12 set. Twelve colors divide its 144 squares, and you win by placing twelve queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
There is exactly one way to finish #285, 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 #285 are: indigo (1 square), pale yellow (2 squares), rose (3 squares), mint (5 squares), sea green (6 squares), amber (11 squares), slate (11 squares), red (16 squares), blue (18 squares), teal (18 squares), khaki (26 squares), orange (27 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the orange region is the roomiest area on the grid with 27 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So indigo, with 1 square, is under far more pressure than orange with 27. A 26-square gap like this one rewards players who start where the choices are fewest.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #285, packing 100% of its 1×1 bounding box, whereas khaki straggles across its 8×8 box at just 41%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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 hard board.
Indigo: 1 square across rows 1–1, columns 7–7. It never leaves row 1, so its queen is locked to that row.
Pale yellow covers 2 squares, spanning 1 row and 2 columns (rows 7–7, columns 1–2). It never leaves row 7, so its queen is locked to that row.
Rose occupies 3 squares within rows 11–12, columns 7–8.
Mint: 5 squares across rows 3–4, columns 8–10.
Sea green covers 6 squares, spanning 3 rows and 3 columns (rows 10–12, columns 1–3).
Amber occupies 11 squares within rows 1–3, columns 7–12.
Slate: 11 squares across rows 2–6, columns 5–8.
Red covers 16 squares, spanning 4 rows and 6 columns (rows 4–7, columns 1–6).
Blue occupies 18 squares within rows 1–4, columns 1–6.
Teal: 18 squares across rows 8–12, columns 1–7.
Khaki covers 26 squares, spanning 8 rows and 8 columns (rows 5–12, columns 3–10).
Orange occupies 27 squares within rows 2–12, columns 9–12.
Where to start on this board
Open on the tightest color. Here that is indigo, confined to 1 square between rows 1 and 1 and columns 7 and 7. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #285.
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. Pale yellow, mint and rose 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 #285
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 8 and 9 are the narrowest, touched by only 3 colors. Columns 11 and 12 are the tightest columns, with 2 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 12 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.
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.
The whole middle game reduces to two sweeps. Sweep the twelve colors looking for one with a single square left; sweep the twelve rows and twelve columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 12x12 solve from a stalled one.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #285 is rated hard
The hard label comes out of four measurable things about #285: three 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 26. Boards that score tight on those measures give up their first queen fast.
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.
Stuck on #285 despite the hard 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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #285, start hunting for it near column 11.
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 #285?
Puzzle #285 is rated hard. 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 #285 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #285, 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 #285?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.