9x9 Queens Puzzle #159
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 #159
What follows is a complete solve of puzzle #159, 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 line confined to one region.
Techniques this board needs: last square in a region, region shadow, region confined to one line, line confined to one region, last square in a column.
Show the full walkthrough (6 steps) — contains the solution
Step 1. Only row 3, column 9 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 9, the rest of the blue region and every square adjacent to it — diagonals included.
Step 2. The orange region is down to one open square, at row 9, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 3, the remaining orange squares, and the ring of neighbours around row 9, column 3.
Step 3. The indigo region has 3 squares left, spread across rows 1 and 2, 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.
The board after step 3 — 2 of 9 queens placed. Step 4. 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 5. Column 8 has only slate squares left (5 open squares). The column needs a queen and only slate can provide one, which pins that colour to this column and kills its squares elsewhere: 9 squares.
Step 6. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: column 7 is down to one square, putting a queen on row 8, column 7; column 6 is down to one square, putting a queen on row 2, column 6; indigo has one square left, so its queen takes row 1, column 1; pale yellow has one square left, so its queen takes row 7, column 2; red has one square left, so its queen takes row 6, column 4; mint has one square left, so its queen takes row 4, column 5; slate has one square left, so its queen takes row 5, column 8. 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 5, column 8.
The board after step 6 — 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 #159
9x9 puzzle #159 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.
Like every board on this site, #159 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 #159 are: blue (1 square), orange (1 square), mint (3 squares), indigo (4 squares), red (8 squares), khaki (9 squares), amber (12 squares), pale yellow (13 squares), slate (30 squares). An even split would hand every color 9 squares, so the blue region is running 8 squares under that average while the slate region is the roomiest area on the grid with 30 squares.
Every color takes one queen and one only, whatever its size — which is why the 29 square difference between blue and slate 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. Blue is the tidiest shape on #159, packing 100% of its 1×1 bounding box, whereas amber straggles across its 4×5 box at just 60%. 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 #159, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Blue: 1 square across rows 3–3, columns 9–9. It never leaves row 3, so its queen is locked to that row.
Orange covers 1 square, spanning 1 row and 1 column (rows 9–9, columns 3–3). It never leaves row 9, so its queen is locked to that row.
Mint occupies 3 squares within rows 3–4, columns 4–5.
Indigo: 4 squares across rows 1–3, columns 1–2.
Red covers 8 squares, spanning 3 rows and 4 columns (rows 5–7, columns 2–5).
Khaki occupies 9 squares within rows 7–9, columns 4–7.
Amber: 12 squares across rows 1–4, columns 2–6.
Pale yellow covers 13 squares, spanning 7 rows and 3 columns (rows 3–9, columns 1–3).
Slate occupies 30 squares within rows 1–9, columns 5–9.
Where to start on this board
Blue is the natural opening on #159: it is the smallest region on the grid at 1 square, boxed into rows 3–3 and columns 9–9. 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 blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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 mint 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 #159
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 5, 6 and 8 are the narrowest, touched by only 3 colors. Column 8 is the tightest column, with 1 color.
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 3 is the crowded extreme at 6 colors — worth revisiting later, not now.
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 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.
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 #159 is rated medium
The rating reflects how much the board concedes up front. Puzzle #159 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 29 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
If #159 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 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.
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 #159 is column 8.
A non-spoiling distribution check: solved, #159 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 #159?
Puzzle #159 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 #159 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #159, 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 #159?
Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.