12x12 Queens Puzzle #182
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #182
What follows is a complete solve of puzzle #182, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 12 queen placements and 4 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, last square in a column.
Show the full walkthrough (6 steps) — contains the solution
Step 1. Wherever indigo ends up among its 3 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
Step 2. All of the red region's remaining squares (3 open squares) lie in column 12. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 10 squares come off.
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: sea green has one square left, so its queen takes row 10, column 11; amber has one square left, so its queen takes row 2, column 10; indigo has one square left, so its queen takes row 1, column 6; pale yellow has one square left, so its queen takes row 7, column 9; blue has one square left, so its queen takes row 3, column 8; rose has one square left, so its queen takes row 12, column 7; teal has one square left, so its queen takes row 11, column 5; orange has one square left, so its queen takes row 9, 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 9, column 4.
The board after step 3 — 8 of 12 queens placed. Step 4. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 3 squares in all.
Step 5. The slate region has 3 squares left, spread across rows 5 and 6, columns 1–3. 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 6. 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: column 3 is down to one square, putting a queen on row 5, column 3; mint has one square left, so its queen takes row 4, column 1; red has one square left, so its queen takes row 6, column 12; khaki has one square left, so its queen takes row 8, column 2. 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 2.
The board after step 6 — 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 #182
Board #182 of the 12x12 bank carries a hard rating. Its 144 squares are shared between twelve colored regions, and the solution places twelve queens: one per row, one per column, one per region, none of them side by side or corner to corner.
Puzzle #182 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 #182 are: indigo (3 squares), red (3 squares), sea green (5 squares), amber (10 squares), pale yellow (10 squares), orange (13 squares), mint (14 squares), blue (15 squares), rose (16 squares), khaki (17 squares), teal (17 squares), slate (21 squares). An even split would hand every color 12 squares, so the indigo region is running 9 squares under that average while the slate region is the roomiest area on the grid with 21 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 indigo, with 3 squares, is under far more pressure than slate with 21. A 18-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Red is the densest region on this grid at 100% of a 3×1 frame; khaki is the loosest, occupying only 40% of its 7×6 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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.
Indigo occupies 3 squares within rows 1–2, columns 6–7.
Red: 3 squares across rows 5–7, columns 12–12. It sits wholly inside column 12, so its queen must be in that column.
Sea green covers 5 squares, spanning 4 rows and 2 columns (rows 9–12, columns 11–12).
Amber occupies 10 squares within rows 1–5, columns 10–12.
Pale yellow: 10 squares across rows 6–10, columns 9–12.
Orange covers 13 squares, spanning 6 rows and 5 columns (rows 7–12, columns 1–5).
Mint occupies 14 squares within rows 1–4, columns 1–5.
Blue: 15 squares across rows 1–6, columns 7–10.
Rose covers 16 squares, spanning 5 rows and 5 columns (rows 8–12, columns 7–11).
Khaki occupies 17 squares within rows 5–11, columns 1–6.
Teal: 17 squares across rows 6–12, columns 4–8.
Slate covers 21 squares, spanning 5 rows and 8 columns (rows 3–7, columns 1–8).
Where to start on this board
Indigo is the natural opening on #182: it is the smallest region on the grid at 3 squares, boxed into rows 1–2 and columns 6–7. Since one of those squares must hold a queen, that block of 2 rows and 2 columns is the most contested part of the board.
With 2 rows and 2 columns of room, indigo needs narrowing rather than solving outright. Test its 3 squares against the neighbours: a candidate that would strand another color is dead, and eliminating even two of them tightens the whole corner of the board around rows 1–2.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: indigo and sea green 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 #182
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 4 and 12 are the narrowest, touched by only 4 colors. Column 9 is the tightest column, with 3 colors.
A line with few colors is a line close to resolving. Where only 4 colors appear, one of them owns the row outright and the others must fit into the remaining 11 rows. Row 10 is the crowded extreme at 6 colors — worth revisiting later, not now.
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.
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 #182 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 #182 is rated hard
The hard label comes out of four measurable things about #182: one of its regions is locked to one row or column, its smallest color spans 3 squares, its least crowded row meets 4 colors, and its largest and smallest regions differ by 18. Boards that score tight on those measures give up their first queen fast.
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.
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 #182, start hunting for it near column 9.
A non-spoiling distribution check: solved, #182 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 #182?
Puzzle #182 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 4 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #182 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #182, 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 #182?
Start with the indigo region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 6–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.