12x12 Queens Puzzle #246
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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #246
What follows is a complete solve of puzzle #246, 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 pairing argument on columns.
Techniques this board needs: last square in a region, region confined to one line, pairing argument on columns.
Show the full walkthrough (5 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: orange has one square left, so its queen takes row 9, column 12; mint has one square left, so its queen takes row 4, column 11; 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. 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 10, column 1.
Step 2. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 6 squares in all.
Step 3. All of the rose region's remaining squares (2 open squares) lie in row 12. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
The board after step 3 — 4 of 12 queens placed. Step 4. Amber and rose are now boxed into columns 2 and 3 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 8 squares at once.
Step 5. 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 6; pale yellow has one square left, so its queen takes row 7, column 10; red has one square left, so its queen takes row 6, column 4; slate has one square left, so its queen takes row 5, column 9; indigo has one square left, so its queen takes row 1, column 8; blue has one square left, so its queen takes row 3, column 7; amber has one square left, so its queen takes row 2, column 2; rose has one square left, so its queen takes row 12, 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 12, column 3.
The board after step 5 — 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 #246
Board #246 of the 12x12 bank carries a hard rating. Its 144 squares are shared between twelve colored regions, and the solution places twelve queens: one per row, one per column, one per region, none of them side by side or corner to corner.
As with every puzzle in this collection, #246 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #246 are: orange (1 square), teal (1 square), sea green (3 squares), mint (5 squares), indigo (6 squares), rose (9 squares), red (10 squares), amber (11 squares), slate (13 squares), blue (27 squares), khaki (28 squares), pale yellow (30 squares). An even split would hand every color 12 squares, so the orange region is running 11 squares under that average while the pale yellow region is the roomiest area on the grid with 30 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 orange, with 1 square, is under far more pressure than pale yellow with 30. A 29-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Orange is the densest region on this grid at 100% of a 1×1 frame; slate is the loosest, occupying only 43% of its 6×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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.
Orange: 1 square across rows 9–9, columns 12–12. It never leaves row 9, so its queen is locked to that row.
Teal covers 1 square, spanning 1 row and 1 column (rows 11–11, columns 5–5). It never leaves row 11, so its queen is locked to that row.
Sea green occupies 3 squares within rows 9–11, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Mint: 5 squares across rows 2–5, columns 11–12.
Indigo covers 6 squares, spanning 2 rows and 5 columns (rows 1–2, columns 8–12).
Rose occupies 9 squares within rows 10–12, columns 1–5.
Red: 10 squares across rows 5–8, columns 3–7.
Amber covers 11 squares, spanning 5 rows and 3 columns (rows 1–5, columns 1–3).
Slate occupies 13 squares within rows 2–7, columns 7–11.
Blue: 27 squares across rows 1–5, columns 3–9.
Khaki covers 28 squares, spanning 8 rows and 8 columns (rows 5–12, columns 1–8).
Pale yellow occupies 30 squares within rows 5–12, columns 7–12.
Where to start on this board
Orange is the natural opening on #246: it is the smallest region on the grid at 1 square, boxed into rows 9–9 and columns 12–12. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. 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 and indigo 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 #246
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 12 are the narrowest, touched by only 3 colors. Columns 2, 6 and 10 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 5 meets 7 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.
Keep alternating between two views of the board. In the region view you ask which of the twelve colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 12x12 board unwinds.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #246 is rated hard
The hard label comes out of four measurable things about #246: 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 29. 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.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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 #246, start hunting for it near row 1.
As a sanity check rather than a spoiler: the finished solution to #246 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 #246?
Puzzle #246 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 #246 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #246, 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 #246?
Start with the orange region — the most constrained color on this board, with 1 square spanning rows 9–9 and columns 12–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.