9x9 Queens Puzzle #258
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #258
What follows is a complete solve of puzzle #258, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 9 queen placements and 11 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, region confined to one line, line confined to one region, last square in a column, pairing argument on columns.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Only row 1, column 9 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 9, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The orange region is down to one open square, at row 9, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 1, the remaining orange squares, and the ring of neighbours around row 9, column 1.
Step 3. The amber region has 3 squares left, spread across rows 2 and 3, columns 6 and 7. 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. Wherever mint 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.
Step 5. Slate is down to 4 candidates in rows 3–6, columns 7 and 8, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about slate itself.
The board after step 5 — 2 of 9 queens placed. Step 6. 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: 4 squares come off.
Step 7. Blue cannot leave row 3 — every one of its open squares (3 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 3 squares in all.
Step 8. All of the khaki region's remaining squares (3 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
Step 9. 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: 5 squares in all.
Step 10. Wherever slate ends up among its 2 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 10 — 2 of 9 queens placed. Step 11. Mint is down to 2 candidates in rows 4 and 5, columns 5 and 6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about mint itself.
Step 12. Every open square left in row 6 (4 open squares) belongs to the red region. Since that row must contain a queen, red is the colour that supplies it — so red squares anywhere else on the board are out, 4 squares in all.
Step 13. Scan column 2 and only row 6, column 2 remains — a red square. Every column takes a queen, so it takes this one. Row 6 and column 2 are now spoken for, along with the squares touching that queen.
Step 14. Here is the pairing argument. The slate and pale yellow regions have no open squares outside columns 7 and 8 — 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: 1 square come off in one stroke.
Step 15. 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: amber has one square left, so its queen takes row 2, column 6; mint has one square left, so its queen takes row 4, column 5; blue has one square left, so its queen takes row 3, column 3; slate has one square left, so its queen takes row 5, column 7; pale yellow has one square left, so its queen takes row 7, column 8; 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.
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 #258
Board #258 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, #258 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 #258 are: indigo (1 square), orange (1 square), mint (3 squares), amber (7 squares), khaki (8 squares), slate (10 squares), blue (12 squares), pale yellow (14 squares), red (25 squares). An even split would hand every color 9 squares, so the indigo region is running 8 squares under that average while the red region is the roomiest area on the grid with 25 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; red has 25. The spread between them on this board is 24 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. Indigo is the tidiest shape on #258, packing 100% of its 1×1 bounding box, whereas slate straggles across its 6×3 box at just 56%. 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.
Indigo: 1 square across rows 1–1, columns 9–9. 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 1–1). It never leaves row 9, so its queen is locked to that row.
Mint occupies 3 squares within rows 4–5, columns 5–6.
Amber: 7 squares across rows 1–3, columns 4–7.
Khaki covers 8 squares, spanning 2 rows and 5 columns (rows 8–9, columns 2–6).
Slate occupies 10 squares within rows 1–6, columns 7–9.
Blue: 12 squares across rows 1–3, columns 1–6.
Pale yellow covers 14 squares, spanning 5 rows and 4 columns (rows 5–9, columns 6–9).
Red occupies 25 squares within rows 3–8, columns 1–6.
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 9 and 9. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #258.
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, mint and khaki 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 #258
A quick way to find the next move is to count how many different colors touch each line. On this board, row 7 is the narrowest, touched by only 2 colors. Column 8 is the tightest column, with 2 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 8 rows. Row 5 is the crowded extreme at 4 colors — worth revisiting later, not now.
Working through the middle game
The middle of #258 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
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.
Resist the plausible-looking queen. On #258 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #258 is rated medium
Ratings track how generous the opening is. On #258 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 24-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
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 #258 the place to look for one is around row 7.
A non-spoiling distribution check: solved, #258 carries 2 queens on the perimeter against 7 queens inside, 2 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 #258?
Puzzle #258 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #258 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #258, 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 #258?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.