12x12 Queens Puzzle #190
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 31-step reasoning is written out below.
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Step-by-step solution for puzzle #190
What follows is a complete solve of puzzle #190, worked the way a person works it rather than the way a computer does. It runs to 31 deductions — 12 queen placements and 19 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 proof by contradiction.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows, proof by contradiction, line confined to one region, last square in a column.
Show the full walkthrough (22 steps) — contains the solution
Step 1. Only row 8, column 12 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 12, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 2. All of the mint region's remaining squares (2 open squares) lie in row 4. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 13 squares come off.
Step 3. Teal cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to teal, so every square in it owned by another colour is dead: 10 squares in all.
Step 4. Wherever amber 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 5. Teal and rose are now boxed into rows 11 and 12 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 13 squares at once.
Step 6. The orange region has 4 squares left, spread across rows 9 and 10, columns 4–6. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
The board after step 6 — 1 of 12 queens placed. Step 7. Orange and sea green are now boxed into rows 9 and 10 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 5 squares at once.
Step 8. Red is down to 3 candidates in rows 6 and 7, columns 5 and 6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about red itself.
Step 9. Indigo, amber, and blue are now boxed into rows 1–3 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 6 squares at once.
Step 10. Wherever pale yellow ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 11. Test row 1, column 4 for indigo: place a queen there, run the forced consequences through, and the rose region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
The board after step 11 — 1 of 12 queens placed. Step 12. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 5. Follow the forced moves that would create and the rose region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 13. Test row 1, column 6 for indigo: place a queen there, run the forced consequences through, and the pale yellow region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 14. Now a short proof by contradiction. Suppose the indigo queen went to row 2, column 4. Follow the forced moves that would create and the rose region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 15. Test row 2, column 5 for indigo: place a queen there, run the forced consequences through, and the pale yellow region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 16. Now a short proof by contradiction. Suppose the indigo queen went to row 2, column 6. Follow the forced moves that would create and the orange region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 17. Test row 3, column 4 for indigo: place a queen there, run the forced consequences through, and the rose region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
The board after step 17 — 1 of 12 queens placed. Step 18. 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: indigo has one square left, so its queen takes row 1, column 7; amber has one square left, so its queen takes row 2, column 2; blue has one square left, so its queen takes row 3, column 9; mint has one square left, so its queen takes row 4, column 11. 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 11.
Step 19. Wherever pale yellow 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. Red cannot leave column 6 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 3 squares in all.
Step 21. Every open square left in row 5 (4 open squares) belongs to the slate region. Since that row must contain a queen, slate is the colour that supplies it — so slate squares anywhere else on the board are out, 4 squares in all.
Step 22. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: column 10 is down to one square, putting a queen on row 10, column 10; orange has one square left, so its queen takes row 9, column 4; pale yellow has one square left, so its queen takes row 7, column 3; red has one square left, so its queen takes row 6, column 6; slate has one square left, so its queen takes row 5, column 8; rose has one square left, so its queen takes row 12, column 5; teal has one square left, so its queen takes row 11, 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 11, column 1.
The board after step 22 — 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 #190
Board #190 of the 12x12 bank carries a medium 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.
As with every puzzle in this collection, #190 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #190 are: khaki (1 square), teal (2 squares), mint (5 squares), amber (6 squares), red (7 squares), rose (7 squares), indigo (8 squares), orange (10 squares), blue (14 squares), sea green (23 squares), pale yellow (24 squares), slate (37 squares). An even split would hand every color 12 squares, so the khaki region is running 11 squares under that average while the slate region is the roomiest area on the grid with 37 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 khaki, with 1 square, is under far more pressure than slate with 37. A 36-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Khaki is the densest region on this grid at 100% of a 1×1 frame; slate is the loosest, occupying only 53% of its 7×10 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 medium board.
Khaki covers 1 square, spanning 1 row and 1 column (rows 8–8, columns 12–12). It never leaves row 8, so its queen is locked to that row.
Teal occupies 2 squares within rows 11–12, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Mint: 5 squares across rows 3–5, columns 10–12.
Amber covers 6 squares, spanning 3 rows and 3 columns (rows 1–3, columns 1–3).
Red occupies 7 squares within rows 6–9, columns 5–7.
Rose: 7 squares across rows 11–12, columns 2–6.
Indigo covers 8 squares, spanning 3 rows and 4 columns (rows 1–3, columns 4–7).
Orange occupies 10 squares within rows 8–11, columns 3–6.
Blue: 14 squares across rows 1–3, columns 7–12.
Sea green covers 23 squares, spanning 4 rows and 6 columns (rows 9–12, columns 7–12).
Pale yellow occupies 24 squares within rows 2–10, columns 1–5.
Slate: 37 squares across rows 3–9, columns 3–12.
Where to start on this board
Khaki is the natural opening on #190: it is the smallest region on the grid at 1 square, boxed into rows 8–8 and columns 12–12. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because khaki never leaves row 8, its queen must be in that row — and that instantly settles row 8 for everyone else. Sweep along it and X out every square that is not khaki. 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. Teal and rose 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 #190
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 4, 5, 6, 7, 10 and 12 are the narrowest, touched by only 3 colors. Columns 1, 2, 8 and 9 are the tightest columns, with 3 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 3 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.
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.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #190 is rated medium
The medium label comes out of four measurable things about #190: three of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 36. 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.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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 #190, start hunting for it near row 1.
A non-spoiling distribution check: solved, #190 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 #190?
Puzzle #190 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #190 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #190, 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 #190?
Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 12–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.