9x9 Queens Puzzle #300
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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #300
What follows is a complete solve of puzzle #300, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 9 queen placements and 8 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 region shadow.
Techniques this board needs: region shadow, region confined to one line, last square in a region.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Wherever indigo 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.
Step 2. All of the slate region's remaining squares (3 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 8 squares come off.
Step 3. Red cannot leave column 9 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 9 squares in all.
Step 4. The indigo region is down to one open square, at row 1, column 8. Every colour holds exactly one queen, so that square is forced. Row 1 and column 8 are now spoken for, along with the squares touching that queen.
The board after step 4 — 1 of 9 queens placed. Step 5. Amber cannot leave column 1 — every one of its open squares (3 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 6. All of the blue region's remaining squares (3 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 7. Pale yellow cannot leave column 4 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 9 squares in all.
Step 8. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
The board after step 8 — 1 of 9 queens placed. Step 9. Only row 7, column 4 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 4, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 10. The red region is down to one open square, at row 6, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 9, the remaining red squares, and the ring of neighbours around row 6, column 9.
Step 11. Slate cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 2 squares in all.
Step 12. 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 1; 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 7; slate has one square left, so its queen takes row 5, column 2; khaki has one square left, so its queen takes row 8, column 6; orange has one square left, so its queen takes row 9, column 3. 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 3.
The board after step 12 — 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 #300
This is puzzle number 300 in the 9x9 collection, rated hard. The grid holds 81 squares split between nine colored regions, and a finished board carries nine queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
As with every puzzle in this collection, #300 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 #300 are: red (2 squares), pale yellow (2 squares), indigo (3 squares), slate (3 squares), amber (9 squares), blue (14 squares), orange (14 squares), mint (15 squares), khaki (19 squares). An even split would hand every color 9 squares, so the red region is running 7 squares under that average while the khaki region is the roomiest area on the grid with 19 squares.
Every color takes one queen and one only, whatever its size — which is why the 17 square difference between red and khaki is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Square count is only half the story — how a color is arranged counts too. Slate is the tidiest shape on #300, packing 100% of its 3×1 bounding box, whereas blue straggles across its 6×5 box at just 47%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a hard board.
Red: 2 squares across rows 6–7, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.
Pale yellow covers 2 squares, spanning 2 rows and 1 column (rows 7–8, columns 4–4). It sits wholly inside column 4, so its queen must be in that column.
Indigo occupies 3 squares within rows 1–2, columns 8–9.
Slate: 3 squares across rows 4–6, columns 2–2. It sits wholly inside column 2, so its queen must be in that column.
Amber covers 9 squares, spanning 4 rows and 4 columns (rows 1–4, columns 1–4).
Blue occupies 14 squares within rows 1–6, columns 5–9.
Orange: 14 squares across rows 5–9, columns 1–5.
Mint covers 15 squares, spanning 6 rows and 4 columns (rows 1–6, columns 3–6).
Khaki occupies 19 squares within rows 4–9, columns 5–9.
Where to start on this board
Begin where the choices are fewest. On this board that means red, which owns just 2 squares inside a 2×1 window running from row 6 to row 7 and column 9 to column 9. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because red 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. Indigo and pale yellow 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 #300
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 1 and 7 are the tightest columns, 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 6 is the crowded extreme at 6 colors — worth revisiting later, not now.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
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.
Resist the plausible-looking queen. On #300 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 #300 is rated hard
The hard label comes out of four measurable things about #300: three of its regions are locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 2 colors, and its largest and smallest regions differ by 17. Boards that score tight on those measures give up their first queen fast.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #300 is row 9.
A non-spoiling distribution check: solved, #300 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 #300?
Puzzle #300 is rated hard. Its smallest color region holds 2 squares, 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 #300 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #300, 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 #300?
Start with the red region — the most constrained color on this board, with 2 squares spanning rows 6–7 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.