9x9 Queens Puzzle #58
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 #58
What follows is a complete solve of puzzle #58, 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, region confined to one line, pairing argument on rows, proof by contradiction, line confined to one region, last square in a row.
Show the full walkthrough (16 steps) — contains the solution
Step 1. Only row 4, column 9 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 9, the rest of the mint region and every square adjacent to it — diagonals included.
Step 2. The slate region is down to one open square, at row 5, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 5, the remaining slate squares, and the ring of neighbours around row 5, column 5.
Step 3. The blue region has 4 squares left, spread across rows 2 and 3, columns 1–3. 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 4. All of the pale yellow region's remaining squares (3 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 5. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 4 squares in all.
The board after step 5 — 2 of 9 queens placed. Step 6. The amber region has 4 squares left, spread across rows 1, 2, and 6, columns 6–8. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 7. Wherever red ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Here is the pairing argument. The red, pale yellow, khaki, and orange regions have no open squares outside rows 6–9 — 4 colours confined to 4 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 1 square come off in one stroke.
Step 9. Test row 1, column 2 for indigo: place a queen there, run the forced consequences through, and column 7 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 10. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 3. Follow the forced moves that would create and column 7 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 11. Test row 1, column 4 for indigo: place a queen there, run the forced consequences through, and column 7 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
The board after step 11 — 2 of 9 queens placed. Step 12. The indigo region has 2 squares left, spread across rows 1 and 2, columns 4 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 13. Amber cannot leave column 8 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 4 squares in all.
Step 14. Every open square left in row 6 (2 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 15. Red cannot leave row 6 — every one of its open squares (2 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 1 square in all.
Step 16. 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: row 7 is down to one square, putting a queen on row 7, column 1; red has one square left, so its queen takes row 6, column 3; blue has one square left, so its queen takes row 3, column 2; orange has one square left, so its queen takes row 9, column 4; indigo has one square left, so its queen takes row 1, column 6; amber has one square left, so its queen takes row 2, column 8; khaki has one square left, so its queen takes row 8, column 7. 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 7.
The board after step 16 — 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 #58
Board #58 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, #58 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 #58 are: mint (1 square), slate (3 squares), pale yellow (3 squares), blue (8 squares), orange (8 squares), indigo (12 squares), khaki (12 squares), amber (17 squares), red (17 squares). An even split would hand every color 9 squares, so the mint region is running 8 squares under that average while the red 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. Mint has only 1 place to put its queen; red 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.
A region's outline can constrain it more than its size does. Here mint is the most solid, filling 100% of its 1×1 box, and amber the most diffuse at 47% of its 6×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Here is the full footprint of every color on puzzle #58, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Mint covers 1 square, spanning 1 row and 1 column (rows 4–4, columns 9–9). It never leaves row 4, so its queen is locked to that row.
Slate occupies 3 squares within rows 4–5, columns 5–6.
Pale yellow: 3 squares across rows 7–9, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Blue covers 8 squares, spanning 3 rows and 4 columns (rows 2–4, columns 1–4).
Orange occupies 8 squares within rows 7–9, columns 2–5.
Indigo: 12 squares across rows 1–2, columns 1–7.
Khaki covers 12 squares, spanning 4 rows and 4 columns (rows 6–9, columns 6–9).
Amber occupies 17 squares within rows 1–6, columns 4–9.
Red: 17 squares across rows 5–8, columns 1–7.
Where to start on this board
Open on the tightest color. Here that is mint, confined to 1 square between rows 4 and 4 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 #58.
Because mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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. Indigo and slate 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 #58
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 3 are 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 8 is the crowded extreme at 4 colors — worth revisiting later, not now.
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.
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.
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 #58 is rated medium
The rating reflects how much the board concedes up front. Puzzle #58 has three regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 16 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 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 #58 the place to look for one is around row 1.
A non-spoiling distribution check: solved, #58 carries 4 queens on the perimeter against 5 queens inside, with the corners empty. 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 #58?
Puzzle #58 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #58 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #58, 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 #58?
Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.