9x9 Queens Puzzle #269
Difficulty: hard. 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 #269
What follows is a complete solve of puzzle #269, 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 pairing argument on columns.
Techniques this board needs: last square in a region, region shadow, pairing argument on columns, last square in a column, last square in a row.
Show the full walkthrough (5 steps) — contains the solution
Step 1. Only row 1, column 5 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 5, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. Amber is down to 4 candidates in rows 2–4, columns 2 and 3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The red region has 6 squares left, spread across rows 6–9, 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 — 1 of 9 queens placed. Step 4. Here is the pairing argument. The mint and red regions have no open squares outside columns 1 and 2 — 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: 3 squares come off in one stroke.
Step 5. 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: amber has one square left, so its queen takes row 2, column 3; slate has one square left, so its queen takes row 5, column 4; pale yellow has one square left, so its queen takes row 7, column 6; orange has one square left, so its queen takes row 9, column 7; column 2 is down to one square, putting a queen on row 6, column 2; row 8 is down to one square, putting a queen on row 8, column 9; blue has one square left, so its queen takes row 3, column 8; mint has one square left, so its queen takes row 4, 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 4, column 1.
The board after step 5 — 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 #269
Puzzle #269 is one of the hard-rated boards in the 9x9 set. Nine colors divide its 81 squares, and you win by placing nine queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
There is exactly one way to finish #269, 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 nine regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #269 are: indigo (1 square), slate (6 squares), red (6 squares), mint (7 squares), orange (7 squares), amber (9 squares), khaki (12 squares), blue (15 squares), pale yellow (18 squares). An even split would hand every color 9 squares, so the indigo region is running 8 squares under that average while the pale yellow region is the roomiest area on the grid with 18 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So indigo, with 1 square, is under far more pressure than pale yellow with 18. A 17-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×1 frame; pale yellow is the loosest, occupying only 50% of its 6×6 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Here is the full footprint of every color on puzzle #269, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo occupies 1 square within rows 1–1, columns 5–5. It never leaves row 1, so its queen is locked to that row.
Slate: 6 squares across rows 3–6, columns 3–4.
Red covers 6 squares, spanning 4 rows and 2 columns (rows 6–9, columns 1–2).
Mint occupies 7 squares within rows 1–6, columns 1–2.
Orange: 7 squares across rows 6–9, columns 6–7.
Amber covers 9 squares, spanning 4 rows and 4 columns (rows 1–4, columns 2–5).
Khaki occupies 12 squares within rows 4–9, columns 8–9.
Blue: 15 squares across rows 1–4, columns 5–9.
Pale yellow covers 18 squares, spanning 6 rows and 6 columns (rows 4–9, columns 2–7).
Where to start on this board
The most constrained color is where a solve should begin, and on #269 that is indigo with 1 square. It reaches from row 1 to row 1 and from column 5 to column 5 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: mint, slate, khaki and red 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 #269
A quick way to find the next move is to count how many different colors touch each line. On this board, row 2 is the narrowest, touched by only 3 colors. Columns 1, 8 and 9 are the tightest columns, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 8 rows. Row 6, meeting 6 colors, is the opposite case — the busiest line on #269 and the last one you should expect to crack.
Working through the middle game
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
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 #269 is rated hard
The rating reflects how much the board concedes up front. Puzzle #269 has two 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 17 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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 hard board from the rest.
Stuck on #269 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 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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #269, start hunting for it near column 1.
Here is a shape check that gives nothing away: when #269 is solved, 4 queens sit on the outer edge of the grid and 5 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #269?
Puzzle #269 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #269 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #269, 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 #269?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.