12x12 Queens Puzzle #187
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #187
What follows is a complete solve of puzzle #187, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 12 queen placements and 6 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 confined to one line, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 10, column 7 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 7, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 2. The teal region is down to one open square, at row 11, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 3, the remaining teal squares, and the ring of neighbours around row 11, column 3.
Step 3. Indigo cannot leave row 1 — every one of its open squares (5 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 5 squares in all.
Step 4. All of the amber region's remaining squares (3 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 9 squares come off.
Step 5. Only row 4, column 8 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 8, the rest of the mint region and every square adjacent to it — diagonals included.
The board after step 5 — 3 of 12 queens placed. Step 6. The rose region is down to one open square, at row 12, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 12 and column 6, the remaining rose squares, and the ring of neighbours around row 12, column 6.
Step 7. Khaki and orange are now boxed into rows 8 and 9 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 6 squares at once.
Step 8. Here is the pairing argument. The indigo, amber, red, and pale yellow regions have no open squares outside columns 9–12 — 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: 5 squares come off in one stroke.
Step 9. Only row 9, column 5 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 5, the rest of the orange region and every square adjacent to it — diagonals included.
The board after step 9 — 5 of 12 queens placed. Step 10. The khaki region is down to one open square, at row 8, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 1, the remaining khaki squares, and the ring of neighbours around row 8, column 1.
Step 11. Only row 5, column 2 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 2, in slate and in the ring around that square is now dead.
Step 12. All of the red region's remaining squares (2 open squares) lie in column 12. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 13. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 1 square in all.
Step 14. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: amber has one square left, so its queen takes row 2, column 11; indigo has one square left, so its queen takes row 1, column 9; red has one square left, so its queen takes row 6, column 12; pale yellow has one square left, so its queen takes row 7, column 10; blue has one square left, so its queen takes row 3, 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 3, column 4.
The board after step 14 — 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 #187
12x12 puzzle #187 is rated medium. 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 #187 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 #187 are: sea green (1 square), teal (1 square), amber (3 squares), indigo (6 squares), red (7 squares), rose (8 squares), mint (9 squares), slate (14 squares), khaki (15 squares), pale yellow (20 squares), blue (29 squares), orange (31 squares). An even split would hand every color 12 squares, so the sea green region is running 11 squares under that average while the orange region is the roomiest area on the grid with 31 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Sea green is working with 1 square while orange has 31 to spare, a gap of 30. 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 indigo is the most solid, filling 100% of its 1×6 box, and mint the most diffuse at 50% of its 6×3 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Here is the full footprint of every color on puzzle #187, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Sea green covers 1 square, spanning 1 row and 1 column (rows 10–10, columns 7–7). It never leaves row 10, so its queen is locked to that row.
Teal occupies 1 square within rows 11–11, columns 3–3. It never leaves row 11, so its queen is locked to that row.
Amber: 3 squares across rows 2–2, columns 10–12. It never leaves row 2, so its queen is locked to that row.
Indigo covers 6 squares, spanning 1 row and 6 columns (rows 1–1, columns 7–12). It never leaves row 1, so its queen is locked to that row.
Red occupies 7 squares within rows 3–6, columns 10–12.
Rose: 8 squares across rows 10–12, columns 6–9.
Mint covers 9 squares, spanning 6 rows and 3 columns (rows 1–6, columns 6–8).
Slate occupies 14 squares within rows 1–9, columns 1–3.
Khaki: 15 squares across rows 7–12, columns 1–4.
Pale yellow covers 20 squares, spanning 7 rows and 5 columns (rows 2–8, columns 8–12).
Blue occupies 29 squares within rows 1–8, columns 2–7.
Orange: 31 squares across rows 7–12, columns 3–12.
Where to start on this board
Begin where the choices are fewest. On this board that means sea green, which owns just 1 square inside a 1×1 window running from row 10 to row 10 and column 7 to column 7. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. 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. Indigo, amber 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 #187
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 9 and 12 are the narrowest, touched by only 3 colors. Columns 1 and 5 are the tightest columns, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 11 rows. By contrast row 8 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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 #187 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 #187 is rated medium
The rating reflects how much the board concedes up front. Puzzle #187 has six regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 30 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
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.
As a sanity check rather than a spoiler: the finished solution to #187 puts 4 queens on the outer border and 8 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #187?
Puzzle #187 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and six of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #187 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #187, 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 #187?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.