9x9 Queens Puzzle #234
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 12-step reasoning is written out below.
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Step-by-step solution for puzzle #234
What follows is a complete solve of puzzle #234, worked the way a person works it rather than the way a computer does. It runs to 12 deductions — 9 queen placements and 3 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 shadow, region confined to one line.
Show the full walkthrough (9 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: indigo has one square left, so its queen takes row 1, column 1; orange has one square left, so its queen takes row 9, column 6; pale yellow has one square left, so its queen takes row 7, column 2; khaki has one square left, so its queen takes row 8, 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 8, column 4.
Step 2. Slate is down to 2 candidates in rows 4 and 5, columns 5 and 7, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about slate itself.
Step 3. The red region is down to one open square, at row 6, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 5, the remaining red squares, and the ring of neighbours around row 6, column 5.
The board after step 3 — 5 of 9 queens placed. Step 4. Only row 5, column 7 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 7, in slate and in the ring around that square is now dead.
Step 5. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 6. Blue cannot leave column 3 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 1 square in all.
The board after step 6 — 6 of 9 queens placed. Step 7. The amber region is down to one open square, at row 2, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 8, the remaining amber squares, and the ring of neighbours around row 2, column 8.
Step 8. Only row 4, column 9 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 9, in mint and in the ring around that square is now dead.
Step 9. The blue region is down to one open square, at row 3, column 3. Every colour holds exactly one queen, so that square is forced. Row 3 and column 3 are now spoken for, along with the squares touching that queen.
The board after step 9 — 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 #234
Board #234 of the 9x9 bank carries a medium rating. Its 81 squares are shared between nine colored regions, and the solution places nine 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, #234 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 #234 are: indigo (1 square), orange (1 square), slate (4 squares), pale yellow (5 squares), red (11 squares), khaki (11 squares), amber (15 squares), blue (16 squares), mint (17 squares). An even split would hand every color 9 squares, so the indigo region is running 8 squares under that average while the mint region is the roomiest area on the grid with 17 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 17. 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.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×1 box that encloses it, while blue is the most scattered at 53% of its 6×5 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
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 medium board.
Indigo: 1 square across rows 1–1, columns 1–1. It never leaves row 1, so its queen is locked to that row.
Orange covers 1 square, spanning 1 row and 1 column (rows 9–9, columns 6–6). It never leaves row 9, so its queen is locked to that row.
Slate occupies 4 squares within rows 4–5, columns 5–7.
Pale yellow: 5 squares across rows 7–9, columns 1–2.
Red covers 11 squares, spanning 5 rows and 4 columns (rows 4–8, columns 4–7).
Khaki occupies 11 squares within rows 6–9, columns 2–6.
Amber: 15 squares across rows 1–4, columns 3–9.
Blue covers 16 squares, spanning 6 rows and 5 columns (rows 1–6, columns 1–5).
Mint occupies 17 squares within rows 2–9, columns 7–9.
Where to start on this board
Open on the tightest color. Here that is indigo, confined to 1 square between rows 1 and 1 and columns 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #234.
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. Orange and slate 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 #234
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2 and 3 are the narrowest, touched by only 3 colors. Columns 8 and 9 are the tightest columns, with 2 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 8 rows. Row 4 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
The whole middle game reduces to two sweeps. Sweep the nine colors looking for one with a single square left; sweep the nine rows and nine columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 9x9 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 #234 is rated medium
The medium label comes out of four measurable things about #234: four 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 16. Boards that score tight on those measures give up their first queen fast.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a medium board from the rest.
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 #234 the place to look for one is around column 8.
A non-spoiling distribution check: solved, #234 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 #234?
Puzzle #234 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #234 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #234, 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 #234?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.