12x12 Queens Puzzle #250
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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #250
What follows is a complete solve of puzzle #250, 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, pairing argument on columns.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 2, column 1 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 1, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. 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: 8 squares come off.
Step 3. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 10 squares in all.
Step 4. Wherever mint 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.
The board after step 4 — 1 of 12 queens placed. Step 5. Slate cannot leave row 5 — every one of its open squares (2 open squares) sits there. That row belongs to slate, so every square on it owned by another colour is dead: 13 squares in all.
Step 6. The mint region is down to one open square, at row 4, column 12. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 12, the remaining mint squares, and the ring of neighbours around row 4, column 12.
Step 7. Only row 1, column 11 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 11, in indigo and in the ring around that square is now dead.
Step 8. 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: 7 squares come off.
Step 9. Khaki cannot leave row 8 — every one of its open squares (2 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 11 squares in all.
The board after step 9 — 3 of 12 queens placed. Step 10. All of the orange region's remaining squares (3 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
Step 11. Rose is down to 3 candidates in rows 11 and 12, columns 9 and 10, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about rose itself.
Step 12. Here is the pairing argument. The blue, pale yellow, and rose regions have no open squares outside columns 8–10 — 3 colours confined to 3 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 5 squares come off in one stroke.
Step 13. 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: orange has one square left, so its queen takes row 9, column 5; 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 2; khaki has one square left, so its queen takes row 8, column 7; teal has one square left, so its queen takes row 11, column 6; rose has one square left, so its queen takes row 12, column 10; sea green has one square left, so its queen takes row 10, column 3; pale yellow has one square left, so its queen takes row 7, column 9; blue has one square left, so its queen takes row 3, column 8. 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 3, column 8.
The board after step 13 — 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 #250
Board #250 of the 12x12 bank carries a medium 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, #250 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 #250 are: amber (1 square), khaki (2 squares), mint (5 squares), orange (5 squares), indigo (6 squares), slate (7 squares), rose (8 squares), blue (10 squares), teal (11 squares), red (26 squares), sea green (28 squares), pale yellow (35 squares). An even split would hand every color 12 squares, so the amber region is running 11 squares under that average while the pale yellow region is the roomiest area on the grid with 35 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Amber has only 1 place to put its queen; pale yellow has 35. The spread between them on this board is 34 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Amber is the densest region on this grid at 100% of a 1×1 frame; slate is the loosest, occupying only 47% of its 5×3 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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.
Amber covers 1 square, spanning 1 row and 1 column (rows 2–2, columns 1–1). It never leaves row 2, so its queen is locked to that row.
Khaki occupies 2 squares within rows 8–8, columns 6–7. It never leaves row 8, so its queen is locked to that row.
Mint: 5 squares across rows 3–5, columns 11–12.
Orange covers 5 squares, spanning 1 row and 5 columns (rows 9–9, columns 5–9). It never leaves row 9, so its queen is locked to that row.
Indigo occupies 6 squares within rows 1–2, columns 9–12.
Slate: 7 squares across rows 3–7, columns 1–3.
Rose covers 8 squares, spanning 3 rows and 4 columns (rows 10–12, columns 9–12).
Blue occupies 10 squares within rows 1–3, columns 6–10.
Teal: 11 squares across rows 10–12, columns 5–9.
Red covers 26 squares, spanning 6 rows and 7 columns (rows 1–6, columns 1–7).
Sea green occupies 28 squares within rows 6–12, columns 1–6.
Pale yellow: 35 squares across rows 3–10, columns 5–12.
Where to start on this board
Amber is the natural opening on #250: it is the smallest region on the grid at 1 square, boxed into rows 2–2 and columns 1–1. 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 amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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, orange 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 #250
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 7, 8, 9, 11 and 12 are the narrowest, touched by only 3 colors. Column 4 is the tightest column, with 2 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 3, meeting 5 colors, is the opposite case — the busiest line on #250 and the last one you should expect to crack.
Working through the middle game
The middle of #250 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.
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 #250 is rated medium
Ratings track how generous the opening is. On #250 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.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
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.
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 #250 the place to look for one is around column 4.
Here is a shape check that gives nothing away: when #250 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 #250?
Puzzle #250 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 #250 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #250, 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 #250?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.