12x12 Queens Puzzle #237
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 22-step reasoning is written out below.
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Step-by-step solution for puzzle #237
What follows is a complete solve of puzzle #237, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 12 queen placements and 10 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: region shadow, pairing argument on rows, pairing argument on columns, last square in a region, region confined to one line.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Wherever indigo 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.
Step 2. Amber is down to 3 candidates in rows 1 and 2, columns 11 and 12, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The mint region has 6 squares left, spread across rows 1–5, columns 1 and 2. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 4. Here is the pairing argument. The indigo and amber regions have no open squares outside rows 1 and 2 — 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: 15 squares come off in one stroke.
Step 5. Mint is down to 4 candidates in rows 3–5, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
The board after step 5 — 0 of 12 queens placed. Step 6. The slate region has 5 squares left, spread across rows 3–5, columns 11 and 12. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 7. Amber and slate are now boxed into columns 11 and 12 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 14 squares at once.
Step 8. The khaki region is down to one open square, at row 8, column 10. Every colour holds exactly one queen, so that square is forced. Row 8 and column 10 are now spoken for, along with the squares touching that queen.
Step 9. Only row 9, column 8 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 8, the rest of the orange region and every square adjacent to it — diagonals included.
The board after step 9 — 2 of 12 queens placed. Step 10. All of the red region's remaining squares (3 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 11. Blue, mint, slate, and red are now boxed into rows 3–6 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 9 squares at once.
Step 12. The pale yellow region is down to one open square, at row 7, column 1. Every colour holds exactly one queen, so that square is forced. Row 7 and column 1 are now spoken for, along with the squares touching that queen.
Step 13. Mint cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 4 squares in all.
Step 14. 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: teal has one square left, so its queen takes row 11, column 3; sea green has one square left, so its queen takes row 10, column 6; indigo has one square left, so its queen takes row 1, column 5; amber has one square left, so its queen takes row 2, column 12; slate has one square left, so its queen takes row 5, column 11; mint has one square left, so its queen takes row 4, column 2; red has one square left, so its queen takes row 6, column 9; rose has one square left, so its queen takes row 12, column 7; blue has one square left, so its queen takes row 3, column 4. 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 4.
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 #237
Puzzle #237 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, #237 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 #237 are: indigo (3 squares), amber (3 squares), teal (5 squares), mint (6 squares), slate (8 squares), orange (9 squares), rose (9 squares), khaki (10 squares), pale yellow (13 squares), red (16 squares), blue (29 squares), sea green (33 squares). An even split would hand every color 12 squares, so the indigo region is running 9 squares under that average while the sea green region is the roomiest area on the grid with 33 squares.
Every color takes one queen and one only, whatever its size — which is why the 30 square difference between indigo and sea green is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #237, packing 75% of its 2×2 bounding box, whereas orange straggles across its 4×5 box at just 45%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #237 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Indigo: 3 squares across rows 1–2, columns 5–6.
Amber covers 3 squares, spanning 2 rows and 2 columns (rows 1–2, columns 11–12).
Teal occupies 5 squares within rows 10–12, columns 1–3.
Mint: 6 squares across rows 1–5, columns 1–2.
Slate covers 8 squares, spanning 5 rows and 3 columns (rows 1–5, columns 10–12).
Orange occupies 9 squares within rows 9–12, columns 8–12.
Rose: 9 squares across rows 10–12, columns 2–7.
Khaki covers 10 squares, spanning 5 rows and 3 columns (rows 7–11, columns 10–12).
Pale yellow occupies 13 squares within rows 5–9, columns 1–4.
Red: 16 squares across rows 3–8, columns 8–12.
Blue covers 29 squares, spanning 6 rows and 8 columns (rows 1–6, columns 2–9).
Sea green occupies 33 squares within rows 5–12, columns 2–9.
Where to start on this board
Open on the tightest color. Here that is indigo, confined to 3 squares between rows 1 and 2 and columns 5 and 6. Its queen has nowhere else to go, which means those 2 rows and 2 columns carry more constraint than anywhere else on #237.
Indigo does not collapse onto a single line, so it will not hand you a queen on move one. What it does give you is a short list of 3 candidates. Take each one in turn, imagine the queen there, cross out its row, its column and the eight squares around it, and ask whether any other region is left with nowhere to go. One or two candidates usually fail that test immediately.
Work outward to the other flat regions next. Amber is no more than two rows tall, so its queen is 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 #237
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3, 4, 6, 7, 8, 9 and 12 are the narrowest, touched by only 4 colors. Columns 1 and 7 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 4 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 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
The middle of #237 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 #237 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers no single-line region at all, a 3-square smallest color, a tightest row touched by 4 colors, and a region-size spread of 30. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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 #237 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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #237 is column 1.
As a sanity check rather than a spoiler: the finished solution to #237 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 #237?
Puzzle #237 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 4 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 12x12 puzzle #237 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #237, 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 #237?
Start with the indigo region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 5–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.