12x12 Queens Puzzle #199
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #199
What follows is a complete solve of puzzle #199, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 12 queen placements and 7 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, pairing argument on columns, last square in a row.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 3, column 4 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 4, the rest of the blue region and every square adjacent to it — diagonals included.
Step 2. 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 3. The sea green region has 3 squares left, spread across rows 10 and 11, columns 5 and 8. 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.
Step 4. Here is the pairing argument. The indigo and amber regions have no open squares outside rows 1 and 2 — 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: 8 squares come off in one stroke.
The board after step 4 — 2 of 12 queens placed. Step 5. Mint is down to 4 candidates in rows 4–6, columns 10 and 11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 6. Here is the pairing argument. The amber, mint, red, and teal 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: 12 squares come off in one stroke.
Step 7. Pale yellow, orange, and sea green are now boxed into columns 5, 7, and 8 and nothing else. That is 3 colours needing 3 columns, so they fill those columns between them — which locks every remaining colour out and removes 6 squares at once.
The board after step 7 — 2 of 12 queens placed. Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: indigo has one square left, so its queen takes row 1, column 3; amber has one square left, so its queen takes row 2, column 12; red has one square left, so its queen takes row 6, column 11; mint has one square left, so its queen takes row 4, column 10; teal has one square left, so its queen takes row 11, column 9; sea green has one square left, so its queen takes row 10, column 5. 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 5.
Step 9. Khaki is down to 3 candidates in rows 8 and 9, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about khaki itself.
Step 10. The orange region has 3 squares left, spread across rows 7 and 9, columns 7 and 8. 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.
Step 11. 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: row 8 is down to one square, putting a queen on row 8, column 1; slate has one square left, so its queen takes row 5, column 2; pale yellow has one square left, so its queen takes row 7, column 8; orange has one square left, so its queen takes row 9, column 7. 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 7.
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 #199
12x12 puzzle #199 is rated hard. 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, #199 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 #199 are: blue (1 square), rose (1 square), amber (7 squares), red (9 squares), indigo (10 squares), mint (10 squares), teal (12 squares), sea green (13 squares), khaki (14 squares), pale yellow (20 squares), orange (20 squares), slate (27 squares). An even split would hand every color 12 squares, so the blue region is running 11 squares under that average while the slate region is the roomiest area on the grid with 27 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Blue has only 1 place to put its queen; slate has 27. The spread between them on this board is 26 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here blue is the most solid, filling 100% of its 1×1 box, and teal the most diffuse at 50% of its 4×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
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.
Blue covers 1 square, spanning 1 row and 1 column (rows 3–3, columns 4–4). It never leaves row 3, so its queen is locked to that row.
Rose occupies 1 square within rows 12–12, columns 6–6. It never leaves row 12, so its queen is locked to that row.
Amber: 7 squares across rows 1–3, columns 9–12.
Red covers 9 squares, spanning 7 rows and 2 columns (rows 4–10, columns 11–12).
Indigo occupies 10 squares within rows 1–2, columns 3–8.
Mint: 10 squares across rows 2–6, columns 8–11.
Teal covers 12 squares, spanning 4 rows and 6 columns (rows 9–12, columns 7–12).
Sea green occupies 13 squares within rows 10–12, columns 1–8.
Khaki: 14 squares across rows 7–11, columns 1–4.
Pale yellow covers 20 squares, spanning 7 rows and 5 columns (rows 4–10, columns 7–11).
Orange occupies 20 squares within rows 3–10, columns 4–8.
Slate: 27 squares across rows 1–8, columns 1–5.
Where to start on this board
Begin where the choices are fewest. On this board that means blue, which owns just 1 square inside a 1×1 window running from row 3 to row 3 and column 4 to column 4. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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. Rose and indigo 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 #199
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 11 and 12 are the narrowest, touched by only 3 colors. Columns 1, 2 and 12 are the tightest columns, with 3 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 10 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
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 #199 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 #199 is rated hard
The hard label comes out of four measurable things about #199: four 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 26. Boards that score tight on those measures give up their first queen fast.
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.
If #199 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 #199 the place to look for one is around row 1.
As a sanity check rather than a spoiler: the finished solution to #199 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 #199?
Puzzle #199 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #199 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #199, 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 #199?
Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.