12x12 Queens Puzzle #192
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #192
What follows is a complete solve of puzzle #192, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 12 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 pairing argument on columns.
Techniques this board needs: last square in a region, region shadow, pairing argument on rows, region confined to one line, pairing argument on columns, last square in a row.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 1, column 5 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 5, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. Blue is down to 3 candidates in rows 2 and 3, columns 11 and 12, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 3. The slate region has 2 squares left, spread across rows 4 and 5, columns 11 and 12. You do not need to know which of them takes the queen: every one of those options attacks the same 4 squares, so they can be crossed out now.
Step 4. Wherever blue ends up among its 2 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 4 — 1 of 12 queens placed. Step 5. Pale yellow is down to 5 candidates in rows 4–7, columns 8 and 9, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 6. Here is the pairing argument. The amber, blue, mint, and slate regions have no open squares outside rows 2–5 — 4 colours confined to 4 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 12 squares come off in one stroke.
Step 7. Red cannot leave row 6 — every one of its open squares (2 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 9 squares in all.
The board after step 7 — 1 of 12 queens placed. Step 8. The pale yellow region is down to one open square, at row 7, column 9. Every colour holds exactly one queen, so that square is forced. Row 7 and column 9 are now spoken for, along with the squares touching that queen.
Step 9. Blue and slate are now boxed into columns 11 and 12 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 10 squares at once.
Step 10. Here is the pairing argument. The amber, red, orange, and teal regions have no open squares outside columns 6, 7, 8, and 10 — 4 colours confined to 4 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 8 squares come off in one stroke.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 10 queens fall out in order without any new idea being needed: rose has one square left, so its queen takes row 12, column 4; sea green has one square left, so its queen takes row 10, column 3; row 5 is down to one square, putting a queen on row 5, column 12; blue has one square left, so its queen takes row 3, column 11; row 4 is down to one square, putting a queen on row 4, column 1; khaki has one square left, so its queen takes row 8, column 2; orange has one square left, so its queen takes row 9, column 10; teal has one square left, so its queen takes row 11, column 8; amber has one square left, so its queen takes row 2, column 7; red has one square left, so its queen takes row 6, column 6. 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 6, column 6.
The board after step 11 — 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 #192
This is puzzle number 192 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 #192 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 #192 are: indigo (1 square), slate (3 squares), blue (5 squares), pale yellow (6 squares), sea green (6 squares), red (8 squares), rose (8 squares), mint (14 squares), teal (15 squares), orange (21 squares), amber (22 squares), khaki (35 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the khaki region is the roomiest area on the grid with 35 squares.
Every color takes one queen and one only, whatever its size — which is why the 34 square difference between indigo 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.
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 khaki is the most scattered at 50% of its 10×7 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
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 medium board.
Indigo: 1 square across rows 1–1, columns 5–5. It never leaves row 1, so its queen is locked to that row.
Slate covers 3 squares, spanning 2 rows and 2 columns (rows 4–5, columns 11–12).
Blue occupies 5 squares within rows 1–3, columns 11–12.
Pale yellow: 6 squares across rows 4–7, columns 8–10.
Sea green covers 6 squares, spanning 3 rows and 3 columns (rows 10–12, columns 3–5).
Red occupies 8 squares within rows 4–6, columns 5–8.
Rose: 8 squares across rows 10–12, columns 4–7.
Mint covers 14 squares, spanning 5 rows and 4 columns (rows 1–5, columns 1–4).
Teal occupies 15 squares within rows 9–12, columns 7–12.
Orange: 21 squares across rows 5–10, columns 7–12.
Amber covers 22 squares, spanning 4 rows and 8 columns (rows 1–4, columns 4–11).
Khaki occupies 35 squares within rows 3–12, columns 1–7.
Where to start on this board
The most constrained color is where a solve should begin, and on #192 that is indigo with 1 square. It reaches from row 1 to row 1 and from column 5 to column 5 — 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. Slate 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 #192
A quick way to find the next move is to count how many different colors touch each line. On this board, row 8 is the narrowest, touched by only 2 colors. Columns 1 and 2 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 11 rows. Row 5 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.
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.
Resist the plausible-looking queen. On #192 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 #192 is rated medium
The medium label comes out of four measurable things about #192: two of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 34. Boards that score tight on those measures give up their first queen fast.
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 medium board from the rest.
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 #192 is row 8.
A non-spoiling distribution check: solved, #192 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 #192?
Puzzle #192 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #192 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #192, 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 #192?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.