12x12 Queens Puzzle #254
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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #254
What follows is a complete solve of puzzle #254, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 12 queen placements and 5 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 shadow.
Techniques this board needs: last square in a region, region confined to one line, region shadow.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Only row 10, column 12 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 12, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 2. All of the mint region's remaining squares (2 open squares) lie in row 4. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 13 squares come off.
Step 3. Only row 5, column 1 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 1, in slate and in the ring around that square is now dead.
The board after step 3 — 2 of 12 queens placed. Step 4. The mint region is down to one open square, at row 4, column 3. Every colour holds exactly one queen, so that square is forced. Row 4 and column 3 are now spoken for, along with the squares touching that queen.
Step 5. Teal is down to 3 candidates in rows 11 and 12, columns 10 and 11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about teal itself.
Step 6. 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: 6 squares come off.
Step 7. Only row 11, column 10 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 10, in teal and in the ring around that square is now dead.
The board after step 7 — 4 of 12 queens placed. Step 8. Blue is down to 3 candidates in rows 1–3, columns 9 and 11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 9. Pale yellow cannot leave column 11 — every one of its open squares (3 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 2 squares in all.
Step 10. 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: blue has one square left, so its queen takes row 3, column 9; red has one square left, so its queen takes row 6, column 8; indigo has one square left, so its queen takes row 1, column 7; khaki has one square left, so its queen takes row 8, column 2; pale yellow has one square left, so its queen takes row 7, column 11; rose has one square left, so its queen takes row 12, column 4; amber has one square left, so its queen takes row 2, column 5; orange has one square left, so its queen takes row 9, column 6. 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 6.
The board after step 10 — 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 #254
Board #254 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.
Like every board on this site, #254 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 #254 are: sea green (1 square), mint (2 squares), slate (3 squares), rose (5 squares), indigo (6 squares), teal (8 squares), blue (9 squares), khaki (15 squares), pale yellow (17 squares), amber (18 squares), red (18 squares), orange (42 squares). An even split would hand every color 12 squares, so the sea green region is running 11 squares under that average while the orange region is the roomiest area on the grid with 42 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 sea green, with 1 square, is under far more pressure than orange with 42. A 41-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Mint is the densest region on this grid at 100% of a 1×2 frame; khaki is the loosest, occupying only 47% of its 8×4 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.
Sea green occupies 1 square within rows 10–10, columns 12–12. It never leaves row 10, so its queen is locked to that row.
Mint: 2 squares across rows 4–4, columns 2–3. It never leaves row 4, so its queen is locked to that row.
Slate covers 3 squares, spanning 2 rows and 2 columns (rows 4–5, columns 1–2).
Rose occupies 5 squares within rows 11–12, columns 1–4.
Indigo: 6 squares across rows 1–3, columns 7–9.
Teal covers 8 squares, spanning 3 rows and 4 columns (rows 10–12, columns 9–12).
Blue occupies 9 squares within rows 1–5, columns 9–11.
Khaki: 15 squares across rows 4–11, columns 1–4.
Pale yellow covers 17 squares, spanning 10 rows and 3 columns (rows 1–10, columns 10–12).
Amber occupies 18 squares within rows 1–3, columns 1–7.
Red: 18 squares across rows 3–8, columns 5–10.
Orange covers 42 squares, spanning 7 rows and 9 columns (rows 6–12, columns 2–10).
Where to start on this board
Sea green is the natural opening on #254: it is the smallest region on the grid at 1 square, boxed into rows 10–10 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 sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. 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. Mint, slate 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 #254
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 9 and 12 are the narrowest, touched by only 3 colors. Columns 5, 6, 8, 11 and 12 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 4 meets 6 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 #254 is rated hard
Ratings track how generous the opening is. On #254 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 41-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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 #254 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 #254, start hunting for it near row 9.
As a sanity check rather than a spoiler: the finished solution to #254 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 #254?
Puzzle #254 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 #254 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #254, 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 #254?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 12–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.