9x9 Queens Puzzle #235
Difficulty: medium. Place 9 queens on this 9x9 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 #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 17 deductions — 9 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: region confined to one line, region shadow, pairing argument on columns, last square in a region, last square in a row.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Mint cannot leave column 7 — every one of its open squares (4 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 5 squares in all.
Step 2. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.
Step 3. The pale yellow region has 3 squares left, spread across rows 7 and 8, columns 8 and 9. 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. Wherever khaki 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. Slate and orange are now boxed into columns 1 and 2 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 8 squares at once.
The board after step 5 — 0 of 9 queens placed. Step 6. The indigo region is down to one open square, at row 1, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 3, the remaining indigo squares, and the ring of neighbours around row 1, column 3.
Step 7. Only row 8, column 4 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 4, in khaki and in the ring around that square is now dead.
Step 8. The pale yellow region is down to one open square, at row 7, column 8. Every colour holds exactly one queen, so that square is forced. Row 7 and column 8 are now spoken for, along with the squares touching that queen.
Step 9. The amber region has 4 squares left, spread across rows 2 and 3, columns 5, 6, and 9. 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.
The board after step 9 — 3 of 9 queens placed. Step 10. All of the blue 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: 1 square come off.
Step 11. Look along row 2: one square survives, row 2, column 5, which belongs to amber. A row cannot be left empty, so the queen goes there. That clears row 2, column 5, the rest of the amber region and every square adjacent to it — diagonals included.
Step 12. Row 3 has a single open square left, at column 9 in the blue region. Every row needs a queen, so this one is forced. Cross out the whole of row 3 and column 9, the remaining blue squares, and the ring of neighbours around row 3, column 9.
Step 13. Mint cannot leave column 7 — 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: 2 squares in all.
Step 14. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: red has one square left, so its queen takes row 6, column 6; mint has one square left, so its queen takes row 4, column 7; slate has one square left, so its queen takes row 5, column 2; orange has one square left, so its queen takes row 9, column 1. 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 1.
The board after step 14 — 9 of 9 queens placed.
That completes the board: 9 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 9x9 Queens puzzle #235
9x9 puzzle #235 is rated medium. Nine colored regions cover its 81 squares, and your job is to seat nine queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
As with every puzzle in this collection, #235 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 #235 are: orange (2 squares), mint (4 squares), pale yellow (6 squares), slate (7 squares), khaki (8 squares), indigo (9 squares), blue (13 squares), amber (14 squares), red (18 squares). An even split would hand every color 9 squares, so the orange region is running 7 squares under that average while the red region is the roomiest area on the grid with 18 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 2 places to put its queen; red has 18. The spread between them on this board is 16 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Square count is only half the story — how a color is arranged counts too. Mint is the tidiest shape on #235, packing 100% of its 4×1 bounding box, whereas khaki straggles across its 4×4 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #235, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Orange covers 2 squares, spanning 1 row and 2 columns (rows 9–9, columns 1–2). It never leaves row 9, so its queen is locked to that row.
Mint occupies 4 squares within rows 4–7, columns 7–7. It sits wholly inside column 7, so its queen must be in that column.
Pale yellow: 6 squares across rows 7–9, columns 7–9.
Slate covers 7 squares, spanning 5 rows and 2 columns (rows 4–8, columns 1–2).
Khaki occupies 8 squares within rows 6–9, columns 2–5.
Indigo: 9 squares across rows 1–5, columns 1–3.
Blue covers 13 squares, spanning 6 rows and 4 columns (rows 2–7, columns 6–9).
Amber occupies 14 squares within rows 1–4, columns 3–9.
Red: 18 squares across rows 3–9, columns 3–7.
Where to start on this board
Orange is the natural opening on #235: it is the smallest region on the grid at 2 squares, boxed into rows 9–9 and columns 1–2. Since one of those squares must hold a queen, that block of 1 row and 2 columns is the most contested part of the board.
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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: slate and orange span only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
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 1 is the narrowest, touched by only 2 colors. Columns 1, 4, 5, 6, 8 and 9 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 8 rows. Row 7 is the crowded extreme at 6 colors — worth revisiting later, not now.
Working through the middle game
The middle of #235 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 nine 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 9x9 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 medium
The rating reflects how much the board concedes up front. Puzzle #235 has two regions confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 16 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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 9x9
At 9x9 a full re-scan after every move starts to get slow, so work locally instead. Once a queen goes down, check only the regions, rows and columns that placement actually touched — that is where new information appeared. Fall back to a complete sweep only when the local pass turns up nothing, and your solve times will drop noticeably.
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 1.
A non-spoiling distribution check: solved, #235 carries 3 queens on the perimeter against 6 queens inside, 1 of them cornered. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
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 9x9 Queens puzzle #235?
Puzzle #235 is rated medium. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #235 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #235, has been verified to have exactly one valid arrangement of nine 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 2 squares spanning rows 9–9 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.