9x9 Queens Puzzle #262
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 22-step reasoning is written out below.
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Step-by-step solution for puzzle #262
What follows is a complete solve of puzzle #262, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 9 queen placements and 13 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 proof by contradiction.
Techniques this board needs: last square in a region, region shadow, proof by contradiction, pairing argument on columns, region confined to one line.
Show the full walkthrough (17 steps) — contains the solution
Step 1. Only row 2, column 4 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 4, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. The indigo region is down to one open square, at row 1, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 9, the remaining indigo squares, and the ring of neighbours around row 1, column 9.
Step 3. Only row 9, column 1 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 1, in orange and in the ring around that square is now dead.
Step 4. Wherever mint 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.
The board after step 4 — 3 of 9 queens placed. Step 5. Slate is down to 5 candidates in rows 4–6, columns 7 and 8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
Step 6. The red region has 5 squares left, spread across rows 5–8, columns 2 and 3. 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. Wherever pale yellow ends up among its 3 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
Step 8. Now a short proof by contradiction. Suppose the blue queen went to row 3, column 7. Follow the forced moves that would create and the pale yellow region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 9. Test row 3, column 8 for blue: place a queen there, run the forced consequences through, and the pale yellow region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
The board after step 9 — 3 of 9 queens placed. Step 10. Here is the pairing argument. The blue, mint, red, and pale yellow regions have no open squares outside columns 2, 3, 5, and 6 — 4 colours confined to 4 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 1 square come off in one stroke.
Step 11. Test row 4, column 6 for blue: place a queen there, run the forced consequences through, and row 5 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 12. Now a short proof by contradiction. Suppose the blue queen went to row 5, column 3. Follow the forced moves that would create and row 3 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 13. Wherever blue ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
The board after step 13 — 3 of 9 queens placed. Step 14. Mint is down to 2 candidates in rows 3 and 4, columns 2 and 3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 15. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 3 squares in all.
Step 16. All of the khaki region's remaining squares (2 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 17. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: red has one square left, so its queen takes row 6, column 2; 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 7; blue has one square left, so its queen takes row 3, column 6; pale yellow has one square left, so its queen takes row 7, column 5; khaki has one square left, so its queen takes row 8, 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 8, column 8.
The board after step 17 — 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 #262
Board #262 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, #262 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 #262 are: amber (1 square), orange (1 square), indigo (4 squares), slate (7 squares), pale yellow (10 squares), mint (12 squares), red (14 squares), khaki (14 squares), blue (18 squares). An even split would hand every color 9 squares, so the amber region is running 8 squares under that average while the blue 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. Amber has only 1 place to put its queen; blue has 18. The spread between them on this board is 17 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. Amber is the tidiest shape on #262, packing 100% of its 1×1 bounding box, whereas blue straggles across its 6×6 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Amber covers 1 square, spanning 1 row and 1 column (rows 2–2, columns 4–4). It never leaves row 2, so its queen is locked to that row.
Orange occupies 1 square within rows 9–9, columns 1–1. It never leaves row 9, so its queen is locked to that row.
Indigo: 4 squares across rows 1–2, columns 7–9.
Slate covers 7 squares, spanning 4 rows and 3 columns (rows 3–6, columns 7–9).
Pale yellow occupies 10 squares within rows 6–9, columns 3–6.
Mint: 12 squares across rows 1–4, columns 1–5.
Red covers 14 squares, spanning 6 rows and 3 columns (rows 4–9, columns 1–3).
Khaki occupies 14 squares within rows 5–9, columns 5–9.
Blue: 18 squares across rows 1–6, columns 3–8.
Where to start on this board
Open on the tightest color. Here that is amber, confined to 1 square between rows 2 and 2 and columns 4 and 4. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #262.
Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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 indigo 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 #262
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3, 7 and 8 are the narrowest, touched by only 3 colors. Column 2 is the tightest column, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 8 rows. By contrast row 6 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
Two checks, run alternately, will carry you through the 81 squares of this grid. First: has any of the nine regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 9x9 boards almost always run one of those checks and forget the other.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #262 is rated medium
Ratings track how generous the opening is. On #262 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 17-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
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 #262 the place to look for one is around column 2.
As a sanity check rather than a spoiler: the finished solution to #262 puts 2 queens on the outer border and 7 queens in the interior, 2 of them in an actual corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #262?
Puzzle #262 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 #262 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #262, 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 #262?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.