12x12 Queens Puzzle #238
Difficulty: easy. 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 23-step reasoning is written out below.
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Step-by-step solution for puzzle #238
What follows is a complete solve of puzzle #238, worked the way a person works it rather than the way a computer does. It runs to 23 deductions — 12 queen placements and 11 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 rows.
Techniques this board needs: last square in a region, region shadow, region confined to one line, pairing argument on rows, line confined to one region, last square in a row.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Only row 1, column 12 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 12, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. Slate is down to 5 candidates in rows 5–7, columns 9–11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
Step 3. Khaki cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 11 squares in all.
Step 4. Wherever amber ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Red is down to 3 candidates in rows 6–8, columns 2 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about red itself.
The board after step 5 — 1 of 12 queens placed. 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: 10 squares come off.
Step 7. Khaki, orange, sea green, and teal are now boxed into rows 8–11 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 11 squares at once.
Step 8. All of the red region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 9. Only row 2, column 3 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 3, the rest of the amber region and every square adjacent to it — diagonals included.
Step 10. The sea green region is down to one open square, at row 10, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 4, the remaining sea green squares, and the ring of neighbours around row 10, column 4.
The board after step 10 — 3 of 12 queens placed. Step 11. Pale yellow is down to 3 candidates in rows 6 and 7, columns 8 and 9, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 12. Every open square left in column 5 (5 open squares) belongs to the mint region. Since that column must contain a queen, mint is the colour that supplies it — so mint squares anywhere else on the board are out, 13 squares in all.
Step 13. Column 6 has only teal squares left (2 open squares). The column needs a queen and only teal can provide one, which pins that colour to this column and kills its squares elsewhere: 2 squares.
Step 14. Here is the pairing argument. The red and pale yellow regions have no open squares outside rows 6 and 7 — 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: 5 squares come off in one stroke.
Step 15. 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: slate has one square left, so its queen takes row 5, column 11; rose has one square left, so its queen takes row 12, column 10; blue has one square left, so its queen takes row 3, column 7; mint has one square left, so its queen takes row 4, column 5; row 8 is down to one square, putting a queen on row 8, column 1; red has one square left, so its queen takes row 6, column 2; pale yellow has one square left, so its queen takes row 7, column 8; orange has one square left, so its queen takes row 9, column 9; teal has one square left, so its queen takes row 11, 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 11, column 6.
The board after step 15 — 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 #238
Board #238 of the 12x12 bank carries a easy 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, #238 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 #238 are: indigo (1 square), khaki (2 squares), rose (4 squares), red (8 squares), amber (10 squares), orange (10 squares), slate (11 squares), sea green (11 squares), pale yellow (13 squares), teal (16 squares), blue (20 squares), mint (38 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the mint region is the roomiest area on the grid with 38 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 1 place to put its queen; mint has 38. The spread between them on this board is 37 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and pale yellow the most diffuse at 43% of its 6×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
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 easy board.
Indigo covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 12–12). It never leaves row 1, so its queen is locked to that row.
Khaki occupies 2 squares within rows 8–9, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Rose: 4 squares across rows 11–12, columns 10–12.
Red covers 8 squares, spanning 5 rows and 3 columns (rows 5–9, columns 1–3).
Amber occupies 10 squares within rows 1–4, columns 1–3.
Orange: 10 squares across rows 8–12, columns 7–10.
Slate covers 11 squares, spanning 6 rows and 4 columns (rows 4–9, columns 9–12).
Sea green occupies 11 squares within rows 9–12, columns 1–4.
Pale yellow: 13 squares across rows 6–11, columns 8–12.
Teal covers 16 squares, spanning 4 rows and 5 columns (rows 9–12, columns 4–8).
Blue occupies 20 squares within rows 1–5, columns 6–12.
Mint: 38 squares across rows 1–8, columns 2–9.
Where to start on this board
Indigo is the natural opening on #238: it is the smallest region on the grid at 1 square, boxed into rows 1–1 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 indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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 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 #238
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2 and 3 are the narrowest, touched by only 3 colors. Column 5 is the tightest column, with 2 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 9 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.
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 #238 is rated easy
The easy label comes out of four measurable things about #238: three 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 37. 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.
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 #238 the place to look for one is around column 5.
As a sanity check rather than a spoiler: the finished solution to #238 puts 3 queens on the outer border and 9 queens in the interior, 1 of them in an actual 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 #238?
Puzzle #238 is rated easy. 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 #238 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #238, 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 #238?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 12–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.