9x9 Queens Puzzle #143
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #143
What follows is a complete solve of puzzle #143, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 9 queen placements and 10 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 column.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Only row 9, column 4 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 4, the rest of the orange region and every square adjacent to it — diagonals included.
Step 2. Slate is down to 4 candidates in rows 5–7, columns 8 and 9, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about slate itself.
Step 3. The pale yellow region has 5 squares left, spread across rows 6–8, columns 1, 2, and 5. 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. All of the khaki region's remaining squares (4 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
Step 5. Slate, red, and pale yellow are now boxed into rows 5–7 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 8 squares at once.
The board after step 5 — 1 of 9 queens placed. Step 6. The mint region has 5 squares left, spread across rows 3 and 4, columns 1, 3, 5, and 6. 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. Column 2 has only amber squares left (3 open squares). The column needs a queen and only amber can provide one, which pins that colour to this column and kills its squares elsewhere: 7 squares.
Step 8. Every open square left in column 3 (2 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, 3 squares in all.
Step 9. Mint cannot leave column 3 — 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: 1 square in all.
Step 10. Every open square left in column 1 (2 open squares) belongs to the pale yellow region. Since that column must contain a queen, pale yellow is the colour that supplies it — so pale yellow squares anywhere else on the board are out, 1 square in all.
The board after step 10 — 1 of 9 queens placed. Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: column 5 is down to one square, putting a queen on row 1, column 5; amber has one square left, so its queen takes row 2, column 2; blue has one square left, so its queen takes row 3, column 9; mint has one square left, so its queen takes row 4, column 3; 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.
Step 12. Wherever red ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 13. Only row 8, column 7 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 7, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 14. The red region is down to one open square, at row 6, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 6, the remaining red squares, and the ring of neighbours around row 6, column 6.
Step 15. Only row 7, column 1 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 1, in pale yellow and in the ring around that square is now dead.
The board after step 15 — 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 #143
9x9 puzzle #143 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.
Puzzle #143 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #143 are: orange (1 square), slate (4 squares), blue (5 squares), red (8 squares), khaki (10 squares), pale yellow (11 squares), indigo (12 squares), amber (13 squares), mint (17 squares). An even split would hand every color 9 squares, so the orange 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. Orange 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 khaki region is the most compact color here, filling 100% of the 2×5 box that encloses it, while pale yellow is the most scattered at 55% of its 4×5 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.
Orange occupies 1 square within rows 9–9, columns 4–4. It never leaves row 9, so its queen is locked to that row.
Slate: 4 squares across rows 5–7, columns 8–9.
Blue covers 5 squares, spanning 4 rows and 2 columns (rows 1–4, columns 8–9).
Red occupies 8 squares within rows 5–7, columns 6–8.
Khaki: 10 squares across rows 8–9, columns 5–9.
Pale yellow covers 11 squares, spanning 4 rows and 5 columns (rows 6–9, columns 1–5).
Indigo occupies 12 squares within rows 1–4, columns 4–8.
Amber: 13 squares across rows 1–4, columns 1–5.
Mint covers 17 squares, spanning 5 rows and 6 columns (rows 3–7, columns 1–6).
Where to start on this board
Orange is the natural opening on #143: it is the smallest region on the grid at 1 square, boxed into rows 9–9 and columns 4–4. 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 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. Khaki is no more than two rows tall, so its queen is 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 #143
A quick way to find the next move is to count how many different colors touch each line. On this board, row 8 is the narrowest, touched by only 2 colors. Columns 1, 2, 3, 7 and 9 are the tightest columns, 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 8 rows. Row 7 sits at the far end with 4 colors crossing it; it will almost certainly be among the last to settle.
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.
With nine queens to seat and nine regions competing over 81 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 9x9 boards quickly and players who stall halfway.
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 #143 is rated medium
The medium label comes out of four measurable things about #143: two of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 16. 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.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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 #143 the place to look for one is around row 8.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 5 queens in the middle, and nothing in the corners. 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 9x9 Queens puzzle #143?
Puzzle #143 is rated medium. Its smallest color region holds 1 square, 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 #143 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #143, 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 #143?
Start with the orange region — the most constrained color on this board, with 1 square spanning rows 9–9 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.