9x9 Queens Puzzle #49
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #49
What follows is a complete solve of puzzle #49, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 9 queen placements and 7 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: region confined to one line, last square in a region, region shadow, pairing argument on columns.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 11 squares in all.
Step 2. All of the blue region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 3. Only row 2, column 3 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 3, in amber and in the ring around that square is now dead.
Step 4. The indigo region is down to one open square, at row 1, column 5. Every colour holds exactly one queen, so that square is forced. Row 1 and column 5 are now spoken for, along with the squares touching that queen.
The board after step 4 — 2 of 9 queens placed. Step 5. Only row 3, column 1 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 1, the rest of the blue region and every square adjacent to it — diagonals included.
Step 6. The mint region has 3 squares left, spread across rows 4 and 5, 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 7. Wherever red ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 8. All of the mint region's remaining squares (2 open squares) lie in row 4. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
Step 9. Pale yellow and khaki are now boxed into columns 2 and 4 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 1 square at once.
The board after step 9 — 3 of 9 queens placed. Step 10. The mint region is down to one open square, at row 4, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 6, the remaining mint squares, and the ring of neighbours around row 4, column 6.
Step 11. Only row 6, column 7 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 7, in red and in the ring around that square is now dead.
Step 12. The slate region has 2 squares left, spread across rows 5 and 8, columns 8 and 9. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
Step 13. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: orange has one square left, so its queen takes row 9, column 8; slate has one square left, so its queen takes row 5, column 9; pale yellow has one square left, so its queen takes row 7, column 2; 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 13 — 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 #49
Puzzle #49 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.
As with every puzzle in this collection, #49 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 #49 are: amber (2 squares), indigo (5 squares), blue (5 squares), red (5 squares), slate (10 squares), pale yellow (11 squares), orange (11 squares), khaki (13 squares), mint (19 squares). An even split would hand every color 9 squares, so the amber region is running 7 squares under that average while the mint region is the roomiest area on the grid with 19 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 amber, with 2 squares, is under far more pressure than mint with 19. A 17-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Amber is the densest region on this grid at 100% of a 1×2 frame; pale yellow is the loosest, occupying only 46% of its 6×4 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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 2 squares, spanning 1 row and 2 columns (rows 2–2, columns 2–3). It never leaves row 2, so its queen is locked to that row.
Indigo occupies 5 squares within rows 1–3, columns 3–5.
Blue: 5 squares across rows 1–3, columns 1–2.
Red covers 5 squares, spanning 4 rows and 2 columns (rows 4–7, columns 6–7).
Slate occupies 10 squares within rows 3–8, columns 7–9.
Pale yellow: 11 squares across rows 4–9, columns 1–4.
Orange covers 11 squares, spanning 4 rows and 5 columns (rows 6–9, columns 5–9).
Khaki occupies 13 squares within rows 6–9, columns 2–5.
Mint: 19 squares across rows 1–5, columns 3–9.
Where to start on this board
The most constrained color is where a solve should begin, and on #49 that is amber with 2 squares. It reaches from row 2 to row 2 and from column 2 to column 3 — 1 row by 2 columns. 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 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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: blue, amber 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 #49
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 9 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 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 5 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
The middle of #49 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.
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 #49 is rated hard
Ratings track how generous the opening is. On #49 you get one region pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 3 colors, and a 17-square gap between the largest and smallest regions. Those four numbers largely explain the hard 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 hard 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.
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 #49, start hunting for it near column 1.
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 #49?
Puzzle #49 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #49 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #49, 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 #49?
Start with the amber region — the most constrained color on this board, with 2 squares spanning rows 2–2 and columns 2–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.