12x12 Queens Puzzle #183
Difficulty: easy. 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 24-step reasoning is written out below.
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Step-by-step solution for puzzle #183
What follows is a complete solve of puzzle #183, worked the way a person works it rather than the way a computer does. It runs to 24 deductions — 12 queen placements and 12 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, region confined to one line, pairing argument on rows, pairing argument on columns, last square in a row.
Show the full walkthrough (20 steps) — contains the solution
Step 1. Only row 1, column 12 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 12, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. Amber is down to 3 candidates in rows 2–4, columns 10 and 11, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The red region has 4 squares left, spread across rows 6 and 7, 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 4. Wherever pale yellow ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Orange is down to 6 candidates in rows 9–11, columns 5–8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about orange itself.
The board after step 5 — 1 of 12 queens placed. Step 6. All of the teal region's remaining squares (2 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 13 squares come off.
Step 7. Orange, sea green, teal, and rose are now boxed into rows 9–12 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 10 squares at once.
Step 8. The pale yellow region is down to one open square, at row 7, column 11. Every colour holds exactly one queen, so that square is forced. Row 7 and column 11 are now spoken for, along with the squares touching that queen.
Step 9. Only row 2, column 10 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 10, the rest of the amber region and every square adjacent to it — diagonals included.
Step 10. 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. Cross out the whole of row 6 and column 1, the remaining red squares, and the ring of neighbours around row 6, column 1.
The board after step 10 — 4 of 12 queens placed. Step 11. Blue is down to 3 candidates in rows 3 and 4, columns 2 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 12. The slate region has 2 squares left, spread across rows 3 and 5, columns 8 and 9. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
Step 13. Khaki cannot leave row 8 — every one of its open squares (2 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 5 squares in all.
Step 14. Here is the pairing argument. The teal and rose regions have no open squares outside rows 11 and 12 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 5 squares come off in one stroke.
Step 15. Slate and khaki are now boxed into columns 8 and 9 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 4 squares at once.
The board after step 15 — 4 of 12 queens placed. Step 16. The rose region is down to one open square, at row 12, column 7. Every colour holds exactly one queen, so that square is forced. Row 12 and column 7 are now spoken for, along with the squares touching that queen.
Step 17. Only row 9, column 6 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 6, the rest of the orange region and every square adjacent to it — diagonals included.
Step 18. The teal region is down to one open square, at row 11, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 5, the remaining teal squares, and the ring of neighbours around row 11, column 5.
Step 19. Wherever mint ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 20. 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: row 4 is down to one square, putting a queen on row 4, column 4; blue has one square left, so its queen takes row 3, column 2; slate has one square left, so its queen takes row 5, column 9; khaki has one square left, so its queen takes row 8, column 8; sea green has one square left, so its queen takes row 10, column 3. 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 10, column 3.
The board after step 20 — 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 #183
12x12 puzzle #183 is rated easy. 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.
Like every board on this site, #183 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #183 are: indigo (1 square), teal (2 squares), red (4 squares), amber (6 squares), orange (6 squares), khaki (11 squares), pale yellow (12 squares), rose (12 squares), sea green (14 squares), blue (15 squares), slate (20 squares), mint (41 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the mint region is the roomiest area on the grid with 41 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 1 place to put its queen; mint has 41. The spread between them on this board is 40 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
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 orange is the most scattered at 50% of its 3×4 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
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.
Indigo: 1 square across rows 1–1, columns 12–12. It never leaves row 1, so its queen is locked to that row.
Teal covers 2 squares, spanning 2 rows and 1 column (rows 11–12, columns 5–5). It sits wholly inside column 5, so its queen must be in that column.
Red occupies 4 squares within rows 6–7, columns 1–3.
Amber: 6 squares across rows 1–4, columns 10–11.
Orange covers 6 squares, spanning 3 rows and 4 columns (rows 9–11, columns 5–8).
Khaki occupies 11 squares within rows 7–11, columns 8–11.
Pale yellow: 12 squares across rows 6–12, columns 10–12.
Rose covers 12 squares, spanning 3 rows and 7 columns (rows 10–12, columns 5–11).
Sea green occupies 14 squares within rows 9–12, columns 1–4.
Blue: 15 squares across rows 1–4, columns 1–6.
Slate covers 20 squares, spanning 6 rows and 6 columns (rows 1–6, columns 7–12).
Mint occupies 41 squares within rows 2–9, columns 1–9.
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 1 square inside a 1×1 window running from row 1 to row 1 and column 12 to column 12. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
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. Red 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 #183
A quick way to find the next move is to count how many different colors touch each line. On this board, row 5 is the narrowest, touched by only 2 colors. Columns 4 and 12 are the tightest columns, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 11 rows. Row 11 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
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.
Keep alternating between two views of the board. In the region view you ask which of the twelve colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 12x12 board unwinds.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #183 is rated easy
Ratings track how generous the opening is. On #183 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 40-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
If #183 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #183 the place to look for one is around row 5.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 9 queens in the middle, including 1 in a corner. 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 #183?
Puzzle #183 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #183 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #183, 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 #183?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 12–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.