11x11 Queens Puzzle #209
Difficulty: medium. Place 11 queens on this 11x11 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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #209
What follows is a complete solve of puzzle #209, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 11 queen placements and 4 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 region shadow.
Techniques this board needs: last square in a region, region shadow, region confined to one line, last square in a row.
Show the full walkthrough (7 steps) — contains the solution
Step 1. Only row 3, column 6 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 6, the rest of the blue region and every square adjacent to it — diagonals included.
Step 2. The slate region is down to one open square, at row 5, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 7, the remaining slate squares, and the ring of neighbours around row 5, column 7.
Step 3. The indigo region has 4 squares left, spread across rows 1, 2, and 4, columns 9–11. 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. All of the red region's remaining squares (2 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 10 squares come off.
The board after step 4 — 2 of 11 queens placed. Step 5. Indigo is down to 3 candidates in rows 1, 2, and 4, columns 10 and 11, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about indigo itself.
Step 6. All of the pale yellow region's remaining squares (5 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: teal has one square left, so its queen takes row 11, column 2; amber has one square left, so its queen takes row 2, column 3; sea green has one square left, so its queen takes row 10, column 10; indigo has one square left, so its queen takes row 1, column 11; khaki has one square left, so its queen takes row 8, column 8; red has one square left, so its queen takes row 6, column 9; row 4 is down to one square, putting a queen on row 4, column 4; orange has one square left, so its queen takes row 9, column 5; pale yellow has one square left, so its queen takes row 7, 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 7, column 1.
The board after step 7 — 11 of 11 queens placed.
That completes the board: 11 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 11x11 Queens puzzle #209
Puzzle #209 is one of the medium-rated boards in the 11x11 set. Eleven colors divide its 121 squares, and you win by placing eleven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
There is exactly one way to finish #209, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these eleven regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #209 are: blue (1 square), teal (2 squares), slate (6 squares), pale yellow (6 squares), sea green (6 squares), indigo (7 squares), amber (7 squares), red (9 squares), khaki (12 squares), orange (32 squares), mint (33 squares). An even split would hand every color 11 squares, so the blue region is running 10 squares under that average while the mint region is the roomiest area on the grid with 33 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 blue, with 1 square, is under far more pressure than mint with 33. A 32-square gap like this one rewards players who start where the choices are fewest.
Square count is only half the story — how a color is arranged counts too. Blue is the tidiest shape on #209, packing 100% of its 1×1 bounding box, whereas mint straggles across its 7×9 box at just 52%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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.
Blue occupies 1 square within rows 3–3, columns 6–6. It never leaves row 3, so its queen is locked to that row.
Teal: 2 squares across rows 11–11, columns 1–2. It never leaves row 11, so its queen is locked to that row.
Slate covers 6 squares, spanning 3 rows and 3 columns (rows 3–5, columns 6–8).
Pale yellow occupies 6 squares within rows 5–10, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Sea green: 6 squares across rows 9–11, columns 9–11.
Indigo covers 7 squares, spanning 4 rows and 3 columns (rows 1–4, columns 9–11).
Amber occupies 7 squares within rows 1–4, columns 1–3.
Red: 9 squares across rows 4–7, columns 8–11.
Khaki covers 12 squares, spanning 5 rows and 4 columns (rows 6–10, columns 8–11).
Orange occupies 32 squares within rows 6–11, columns 2–8.
Mint: 33 squares across rows 1–7, columns 2–10.
Where to start on this board
Blue is the natural opening on #209: it is the smallest region on the grid at 1 square, boxed into rows 3–3 and columns 6–6. 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 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. Teal 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 #209
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 8 and 11 are the narrowest, touched by only 3 colors. Columns 4 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 10 rows. By contrast row 7 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
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.
Two checks, run alternately, will carry you through the 121 squares of this grid. First: has any of the eleven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 11x11 boards almost always run one of those checks and forget the other.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #209 is rated medium
Ratings track how generous the opening is. On #209 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 32-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
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.
Stuck on #209 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
Techniques that work well at 11x11
At 11x11 you are managing 121 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 #209, start hunting for it near column 4.
As a sanity check rather than a spoiler: the finished solution to #209 puts 3 queens on the outer border and 8 queens in the interior, 1 of them in an actual 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 11x11 Queens puzzle #209?
Puzzle #209 is rated medium. 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 11x11 puzzle #209 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #209, has been verified to have exactly one valid arrangement of eleven queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #209?
Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.