9x9 Queens Puzzle #1
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 15-step reasoning is written out below.
Step-by-step solution for puzzle #1
What follows is a complete solve of puzzle #1, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 9 queen placements and 6 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 shadow, last square in a region, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Wherever blue ends up among its 5 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 2. The slate region is down to one open square, at row 5, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 9, the remaining slate squares, and the ring of neighbours around row 5, column 9.
Step 3. Only row 3, column 8 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 8, in blue and in the ring around that square is now dead.
The board after step 3 — 2 of 9 queens placed. Step 4. Wherever mint ends up among its 2 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
Step 5. Red is down to 2 candidates in rows 4 and 6, columns 1 and 2, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about red itself.
Step 6. The khaki region has 3 squares left, spread across rows 7 and 8, 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 6 — 2 of 9 queens placed. Step 7. Indigo, amber, mint, and red are now boxed into rows 1, 2, 4, and 6 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 4 squares at once.
Step 8. Here is the pairing argument. The red and khaki 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: 5 squares come off in one stroke.
Step 9. 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: indigo has one square left, so its queen takes row 1, column 4; mint has one square left, so its queen takes row 4, column 3; red has one square left, so its queen takes row 6, column 1; amber has one square left, so its queen takes row 2, column 6; khaki has one square left, so its queen takes row 8, column 2; pale yellow has one square left, so its queen takes row 7, column 5; orange has one square left, so its queen takes row 9, 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 9, column 7.
The board after step 9 — 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 #1
Puzzle #1 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, #1 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 #1 are: slate (2 squares), khaki (3 squares), blue (5 squares), red (5 squares), mint (6 squares), indigo (9 squares), orange (14 squares), amber (18 squares), pale yellow (19 squares). An even split would hand every color 9 squares, so the slate region is running 7 squares under that average while the pale yellow 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 slate, with 2 squares, is under far more pressure than pale yellow 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. Slate is the densest region on this grid at 100% of a 2×1 frame; mint is the loosest, occupying only 50% of its 3×4 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 #1, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Slate covers 2 squares, spanning 2 rows and 1 column (rows 4–5, columns 9–9). It sits wholly inside column 9, so its queen must be in that column.
Khaki occupies 3 squares within rows 7–8, columns 1–2.
Blue: 5 squares across rows 1–4, columns 8–9.
Red covers 5 squares, spanning 3 rows and 3 columns (rows 4–6, columns 1–3).
Mint occupies 6 squares within rows 2–4, columns 2–5.
Indigo: 9 squares across rows 1–4, columns 1–4.
Orange covers 14 squares, spanning 4 rows and 5 columns (rows 6–9, columns 5–9).
Amber occupies 18 squares within rows 1–6, columns 5–8.
Pale yellow: 19 squares across rows 4–9, columns 1–5.
Where to start on this board
The most constrained color is where a solve should begin, and on #1 that is slate with 2 squares. It reaches from row 4 to row 5 and from column 9 to column 9 — 2 rows 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 slate stays inside column 9, its queen belongs to that column and no other region may use it. Cross out the rest of column 9 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
Work outward to the other flat regions next. Khaki is no more than two rows tall, so its queen is 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 #1
A quick way to find the next move is to count how many different colors touch each line. On this board, row 9 is the narrowest, touched by only 2 colors. Columns 6 and 7 are the tightest columns, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 8 rows. Row 4 sits at the far end with 7 colors crossing it; it will almost certainly be among the last to settle.
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.
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 #1 is rated hard
The rating reflects how much the board concedes up front. Puzzle #1 has one region confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 2 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.
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 #1, start hunting for it near row 9.
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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 9x9 Queens puzzle #1?
Puzzle #1 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #1 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #1, 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 #1?
Start with the slate region — the most constrained color on this board, with 2 squares spanning rows 4–5 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.