12x12 Queens Puzzle #245
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 14-step reasoning is written out below.
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Step-by-step solution for puzzle #245
What follows is a complete solve of puzzle #245, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 12 queen placements and 2 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 (6 steps) — contains the solution
Step 1. Only row 6, column 6 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 6, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. The sea green region is down to one open square, at row 10, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 1, the remaining sea green squares, and the ring of neighbours around row 10, column 1.
Step 3. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 10 squares in all.
The board after step 3 — 2 of 12 queens placed. Step 4. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: amber has one square left, so its queen takes row 2, column 12; blue has one square left, so its queen takes row 3, column 10; mint has one square left, so its queen takes row 4, column 2; slate has one square left, so its queen takes row 5, column 4; indigo has one square left, so its queen takes row 1, column 5; orange has one square left, so its queen takes row 9, 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 9, column 11.
Step 5. All of the teal region's remaining squares (2 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 6. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: rose has one square left, so its queen takes row 12, column 9; khaki has one square left, so its queen takes row 8, column 8; teal has one square left, so its queen takes row 11, column 7; pale yellow has one square left, so its queen takes row 7, 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 7, column 3.
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 #245
Puzzle #245 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.
Like every board on this site, #245 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 #245 are: red (1 square), sea green (1 square), indigo (3 squares), amber (3 squares), rose (11 squares), blue (12 squares), mint (13 squares), slate (13 squares), teal (13 squares), orange (17 squares), khaki (22 squares), pale yellow (35 squares). An even split would hand every color 12 squares, so the red region is running 11 squares under that average while the pale yellow region is the roomiest area on the grid with 35 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 red, with 1 square, is under far more pressure than pale yellow with 35. A 34-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 #245, packing 100% of its 1×3 bounding box, whereas khaki straggles across its 9×5 box at just 49%. 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.
Red occupies 1 square within rows 6–6, columns 6–6. It never leaves row 6, so its queen is locked to that row.
Sea green: 1 square across rows 10–10, columns 1–1. It never leaves row 10, so its queen is locked to that row.
Indigo covers 3 squares, spanning 1 row and 3 columns (rows 1–1, columns 4–6). It never leaves row 1, so its queen is locked to that row.
Amber occupies 3 squares within rows 1–2, columns 11–12.
Rose: 11 squares across rows 10–12, columns 8–12.
Blue covers 12 squares, spanning 3 rows and 6 columns (rows 1–3, columns 7–12).
Mint occupies 13 squares within rows 1–4, columns 1–4.
Slate: 13 squares across rows 2–6, columns 3–6.
Teal covers 13 squares, spanning 4 rows and 5 columns (rows 9–12, columns 4–8).
Orange occupies 17 squares within rows 4–10, columns 10–12.
Khaki: 22 squares across rows 3–11, columns 7–11.
Pale yellow covers 35 squares, spanning 8 rows and 8 columns (rows 5–12, columns 1–8).
Where to start on this board
Open on the tightest color. Here that is red, confined to 1 square between rows 6 and 6 and columns 6 and 6. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #245.
Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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. Indigo, sea green and amber 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 #245
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 7, 8 and 12 are the narrowest, touched by only 3 colors. Column 2 is the tightest column, 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 10 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
The middle of #245 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
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 #245 is rated hard
The hard label comes out of four measurable things about #245: 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 34. 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.
If #245 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.
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 #245, start hunting for it near column 2.
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 #245?
Puzzle #245 is rated hard. 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 #245 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #245, 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 #245?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.