12x12 Queens Puzzle #295
Difficulty: hard. 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 13-step reasoning is written out below.
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Step-by-step solution for puzzle #295
What follows is a complete solve of puzzle #295, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 12 queen placements and 1 elimination step 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 confined to one line.
Techniques this board needs: last square in a region, region confined to one line.
Show the full walkthrough (3 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: rose has one square left, so its queen takes row 12, column 3; teal has one square left, so its queen takes row 11, column 10; sea green has one square left, so its queen takes row 10, column 12; orange has one square left, so its queen takes row 9, column 1. 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 1.
Step 2. Slate cannot leave column 2 — every one of its open squares (3 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 4 squares in all.
The board after step 2 — 4 of 12 queens placed. Step 3. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 4; red has one square left, so its queen takes row 6, column 5; khaki has one square left, so its queen takes row 8, column 6; indigo has one square left, so its queen takes row 1, column 7; pale yellow has one square left, so its queen takes row 7, column 11; slate has one square left, so its queen takes row 5, column 2; amber has one square left, so its queen takes row 2, column 9; mint has one square left, so its queen takes row 4, column 8. 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 4, column 8.
The board after step 3 — 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 #295
12x12 puzzle #295 is rated hard. Twelve colored regions cover its 144 squares, and your job is to seat twelve queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Puzzle #295 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 #295 are: rose (1 square), teal (3 squares), blue (5 squares), sea green (6 squares), orange (7 squares), red (8 squares), mint (10 squares), slate (13 squares), indigo (14 squares), pale yellow (20 squares), amber (23 squares), khaki (34 squares). An even split would hand every color 12 squares, so the rose region is running 11 squares under that average while the khaki region is the roomiest area on the grid with 34 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Rose is working with 1 square while khaki has 34 to spare, a gap of 33. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here sea green is the most solid, filling 100% of its 3×2 box, and mint the most diffuse at 50% of its 4×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
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.
Rose covers 1 square, spanning 1 row and 1 column (rows 12–12, columns 3–3). It never leaves row 12, so its queen is locked to that row.
Teal occupies 3 squares within rows 11–12, columns 9–10.
Blue: 5 squares across rows 2–3, columns 2–4.
Sea green covers 6 squares, spanning 3 rows and 2 columns (rows 10–12, columns 11–12).
Orange occupies 7 squares within rows 9–12, columns 1–2.
Red: 8 squares across rows 4–6, columns 2–5.
Mint covers 10 squares, spanning 4 rows and 5 columns (rows 4–7, columns 7–11).
Slate occupies 13 squares within rows 1–9, columns 1–2.
Indigo: 14 squares across rows 1–4, columns 2–7.
Pale yellow covers 20 squares, spanning 6 rows and 6 columns (rows 6–11, columns 7–12).
Amber occupies 23 squares within rows 1–7, columns 7–12.
Khaki: 34 squares across rows 5–12, columns 3–8.
Where to start on this board
Begin where the choices are fewest. On this board that means rose, which owns just 1 square inside a 1×1 window running from row 12 to row 12 and column 3 to column 3. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because rose never leaves row 12, its queen must be in that row — and that instantly settles row 12 for everyone else. Sweep along it and X out every square that is not rose. 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. Blue and teal 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 #295
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 8 are the narrowest, touched by only 3 colors. Columns 1 and 6 are the tightest columns, with 2 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 11 rows. Row 6 is the crowded extreme at 6 colors — worth revisiting later, not now.
Working through the middle game
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
With twelve queens to seat and twelve regions competing over 144 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 12x12 boards quickly and players who stall halfway.
Resist the plausible-looking queen. On #295 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 #295 is rated hard
Ratings track how generous the opening is. On #295 you get two regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 33-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around column 1 on this board.
A non-spoiling distribution check: solved, #295 carries 4 queens on the perimeter against 8 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 12x12 Queens puzzle #295?
Puzzle #295 is rated hard. 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 #295 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #295, 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 #295?
Start with the rose region — the most constrained color on this board, with 1 square spanning rows 12–12 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.