12x12 Queens Puzzle #300
Difficulty: medium. Place 12 queens on this 12x12 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 12-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 12 deductions, every one of them a forced placement. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the last square in a region.
Techniques this board needs: last square in a region.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Only row 1, column 11 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 11, 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 12. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 12, the remaining orange squares, and the ring of neighbours around row 9, column 12.
Step 3. Only row 3, column 10 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 10, in blue and in the ring around that square is now dead.
Step 4. The sea green region is down to one open square, at row 10, column 8. Every colour holds exactly one queen, so that square is forced. Row 10 and column 8 are now spoken for, along with the squares touching that queen.
The board after step 4 — 4 of 12 queens placed. Step 5. Only row 2, column 7 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 7, the rest of the amber region and every square adjacent to it — diagonals included.
Step 6. The mint region is down to one open square, at row 4, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 2, the remaining mint squares, and the ring of neighbours around row 4, column 2.
Step 7. Only row 12, column 9 is still open in rose, and since each colour must take a queen, that settles it. Everything else in row 12, in column 9, in rose and in the ring around that square is now dead.
Step 8. The teal region is down to one open square, at row 11, column 6. Every colour holds exactly one queen, so that square is forced. Row 11 and column 6 are now spoken for, along with the squares touching that queen.
The board after step 8 — 8 of 12 queens placed. Step 9. Only row 8, column 5 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 5, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 10. The slate region is down to one open square, at row 5, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 4, the remaining slate squares, and the ring of neighbours around row 5, column 4.
Step 11. Only row 7, column 3 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 3, in pale yellow and in the ring around that square is now dead.
Step 12. The red region is down to one open square, at row 6, column 1. Every colour holds exactly one queen, so that square is forced. Row 6 and column 1 are now spoken for, along with the squares touching that queen.
The board after step 12 — 12 of 12 queens placed.
That completes the board: 12 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 12x12 Queens puzzle #300
This is puzzle number 300 in the 12x12 collection, rated medium. The grid holds 144 squares split between twelve colored regions, and a finished board carries twelve queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
Puzzle #300 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #300 are: indigo (1 square), orange (4 squares), sea green (4 squares), pale yellow (9 squares), teal (9 squares), mint (10 squares), khaki (11 squares), rose (11 squares), blue (12 squares), amber (19 squares), red (24 squares), slate (30 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the slate region is the roomiest area on the grid with 30 squares.
Every color takes one queen and one only, whatever its size — which is why the 29 square difference between indigo and slate 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.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×1 box that encloses it, while mint is the most scattered at 42% of its 4×6 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
Region by region
Below is every color on #300 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Indigo: 1 square across rows 1–1, columns 11–11. It never leaves row 1, so its queen is locked to that row.
Orange covers 4 squares, spanning 3 rows and 2 columns (rows 8–10, columns 11–12).
Sea green occupies 4 squares within rows 9–10, columns 8–10.
Pale yellow: 9 squares across rows 6–9, columns 3–6.
Teal covers 9 squares, spanning 3 rows and 4 columns (rows 10–12, columns 5–8).
Mint occupies 10 squares within rows 1–4, columns 1–6.
Khaki: 11 squares across rows 7–11, columns 4–7.
Rose covers 11 squares, spanning 3 rows and 4 columns (rows 10–12, columns 9–12).
Blue occupies 12 squares within rows 1–5, columns 10–12.
Amber: 19 squares across rows 1–4, columns 2–9.
Red covers 24 squares, spanning 9 rows and 4 columns (rows 4–12, columns 1–4).
Slate occupies 30 squares within rows 3–8, columns 3–12.
Where to start on this board
The most constrained color is where a solve should begin, and on #300 that is indigo with 1 square. It reaches from row 1 to row 1 and from column 11 to column 11 — 1 row 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 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. Sea green 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 #300
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 5, 6 and 12 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 11 rows. Row 10 sits at the far end with 6 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
The middle of #300 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 144 squares of this grid. First: has any of the twelve regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 12x12 boards almost always run one of those checks and forget the other.
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 #300 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 29. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
Techniques that work well at 12x12
At 12x12 you are managing 144 squares, and holding the whole board in your head will not work. Split it into quadrants and solve locally. Most useful deductions on a grid this large are regional — a color pinched between two placed queens, or a band of rows that two regions must share. Trust the marks on the board over your memory.
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 column 1.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 8 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 12x12 Queens puzzle #300?
Puzzle #300 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #300 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #300, has been verified to have exactly one valid arrangement of twelve 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 indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.