12x12 Queens Puzzle #235
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #235
What follows is a complete solve of puzzle #235, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 12 queen placements and 8 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, line confined to one region, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 9, column 1 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 1, the rest of the orange region and every square adjacent to it — diagonals included.
Step 2. The teal region is down to one open square, at row 11, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 2, the remaining teal squares, and the ring of neighbours around row 11, column 2.
Step 3. Only row 12, column 12 is still open in rose, and since each colour must take a queen, that settles it. Everything else in row 12, in column 12, in rose and in the ring around that square is now dead.
Step 4. 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: 9 squares come off.
The board after step 4 — 3 of 12 queens placed. Step 5. Amber cannot leave column 8 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 10 squares in all.
Step 6. The mint region has 4 squares left, spread across rows 3 and 4, columns 9–11. 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. Wherever slate ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Every open square left in row 10 (7 open squares) belongs to the sea green region. Since that row must contain a queen, sea green is the colour that supplies it — so sea green squares anywhere else on the board are out, 5 squares in all.
Step 9. Amber and blue are now boxed into rows 2 and 3 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 4 squares at once.
The board after step 9 — 3 of 12 queens placed. Step 10. 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: 6 squares come off.
Step 11. Only row 5, column 4 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 4, in slate and in the ring around that square is now dead.
Step 12. Here is the pairing argument. The indigo and khaki regions have no open squares outside columns 10 and 11 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 4 squares come off in one stroke.
Step 13. 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: mint has one square left, so its queen takes row 4, column 9; amber has one square left, so its queen takes row 2, column 8; red has one square left, so its queen takes row 6, column 7; pale yellow has one square left, so its queen takes row 7, column 3; blue has one square left, so its queen takes row 3, column 6; khaki has one square left, so its queen takes row 8, column 11; indigo has one square left, so its queen takes row 1, column 10; sea green has one square left, so its queen takes row 10, column 5. 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 5.
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 #235
12x12 puzzle #235 is rated hard. Twelve colored regions cover its 144 squares, and your job is to seat twelve queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
There is exactly one way to finish #235, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these twelve regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #235 are: orange (1 square), amber (2 squares), rose (2 squares), indigo (3 squares), slate (6 squares), teal (8 squares), red (12 squares), mint (13 squares), khaki (16 squares), blue (19 squares), pale yellow (21 squares), sea green (41 squares). An even split would hand every color 12 squares, so the orange region is running 11 squares under that average while the sea green region is the roomiest area on the grid with 41 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Orange has only 1 place to put its queen; sea green has 41. The spread between them on this board is 40 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×3 box that encloses it, while slate is the most scattered at 50% of its 3×4 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
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.
Orange covers 1 square, spanning 1 row and 1 column (rows 9–9, columns 1–1). It never leaves row 9, so its queen is locked to that row.
Amber occupies 2 squares within rows 2–3, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.
Rose: 2 squares across rows 11–12, columns 12–12. It sits wholly inside column 12, so its queen must be in that column.
Indigo covers 3 squares, spanning 1 row and 3 columns (rows 1–1, columns 10–12). It never leaves row 1, so its queen is locked to that row.
Slate occupies 6 squares within rows 3–5, columns 2–5.
Teal: 8 squares across rows 8–12, columns 1–2.
Red covers 12 squares, spanning 5 rows and 4 columns (rows 4–8, columns 7–10).
Mint occupies 13 squares within rows 1–4, columns 8–12.
Khaki: 16 squares across rows 4–9, columns 9–12.
Blue covers 19 squares, spanning 3 rows and 7 columns (rows 1–3, columns 1–7).
Pale yellow occupies 21 squares within rows 4–8, columns 1–7.
Sea green: 41 squares across rows 7–12, columns 2–12.
Where to start on this board
Begin where the choices are fewest. On this board that means orange, which owns just 1 square inside a 1×1 window running from row 9 to row 9 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
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. Indigo, amber 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 #235
A quick way to find the next move is to count how many different colors touch each line. On this board, row 10 is the narrowest, touched by only 2 colors. Column 6 is the tightest column, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 11 rows. Row 8 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.
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.
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 #235 is rated hard
Ratings track how generous the opening is. On #235 you get five regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 40-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.
Stuck on #235 despite the hard rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 #235 the place to look for one is around row 10.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 9 queens in the middle, including 1 in a corner. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #235?
Puzzle #235 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #235 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #235, 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 #235?
Start with the orange region — the most constrained color on this board, with 1 square spanning rows 9–9 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.