11x11 Queens Puzzle #265
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #265
What follows is a complete solve of puzzle #265, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 11 queen placements and 9 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 rows.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows, last square in a column.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 11, column 6 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 6, the rest of the teal region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 10 squares come off.
Step 3. The slate region has 7 squares left, spread across rows 3–8, columns 2 and 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 orange 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.
The board after step 4 — 1 of 11 queens placed. Step 5. Indigo and amber are now boxed into rows 1 and 2 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 11 squares at once.
Step 6. 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: blue has one square left, so its queen takes row 3, column 2; indigo has one square left, so its queen takes row 1, column 1; amber has one square left, so its queen takes row 2, column 7; slate has one square left, so its queen takes row 5, column 3; sea green has one square left, so its queen takes row 10, 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 10, column 4.
Step 7. Mint is down to 2 candidates in rows 4 and 6, columns 5 and 8, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about mint itself.
Step 8. The orange region has 3 squares left, spread across rows 8 and 9, columns 9 and 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 9. Wherever khaki 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.
The board after step 9 — 6 of 11 queens placed. Step 10. All of the pale yellow 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: 1 square come off.
Step 11. Only row 4, column 8 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 8, in mint and in the ring around that square is now dead.
Step 12. Wherever red 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 13. 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: column 10 is down to one square, putting a queen on row 6, column 10; khaki has one square left, so its queen takes row 8, column 9; pale yellow has one square left, so its queen takes row 7, column 5; orange has one square left, so its queen takes row 9, 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 9, column 11.
The board after step 13 — 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 #265
Puzzle #265 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.
As with every puzzle in this collection, #265 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 #265 are: teal (1 square), indigo (2 squares), amber (6 squares), orange (8 squares), blue (9 squares), slate (12 squares), mint (13 squares), sea green (13 squares), red (14 squares), khaki (16 squares), pale yellow (27 squares). An even split would hand every color 11 squares, so the teal region is running 10 squares under that average while the pale yellow region is the roomiest area on the grid with 27 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 teal, with 1 square, is under far more pressure than pale yellow with 27. A 26-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. Indigo is the tidiest shape on #265, packing 100% of its 2×1 bounding box, whereas mint straggles across its 5×6 box at just 43%. 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.
Teal covers 1 square, spanning 1 row and 1 column (rows 11–11, columns 6–6). It never leaves row 11, so its queen is locked to that row.
Indigo occupies 2 squares within rows 1–2, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Amber: 6 squares across rows 1–2, columns 6–10.
Orange covers 8 squares, spanning 4 rows and 3 columns (rows 8–11, columns 9–11).
Blue occupies 9 squares within rows 1–4, columns 1–4.
Slate: 12 squares across rows 3–8, columns 1–3.
Mint covers 13 squares, spanning 5 rows and 6 columns (rows 2–6, columns 5–10).
Sea green occupies 13 squares within rows 9–11, columns 1–5.
Red: 14 squares across rows 1–7, columns 8–11.
Khaki covers 16 squares, spanning 6 rows and 5 columns (rows 6–11, columns 6–10).
Pale yellow occupies 27 squares within rows 1–9, columns 3–8.
Where to start on this board
Teal is the natural opening on #265: it is the smallest region on the grid at 1 square, boxed into rows 11–11 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 teal never leaves row 11, its queen must be in that row — and that instantly settles row 11 for everyone else. Sweep along it and X out every square that is not teal. 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 and amber 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 #265
A quick way to find the next move is to count how many different colors touch each line. On this board, row 10 is the narrowest, touched by only 3 colors. Column 11 is the tightest column, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 2 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
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 #265 is rated medium
Ratings track how generous the opening is. On #265 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 26-square gap between the largest and smallest regions. Those four numbers largely explain the medium 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.
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 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 #265, start hunting for it near column 11.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 8 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 11x11 Queens puzzle #265?
Puzzle #265 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 11x11 puzzle #265 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #265, 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 #265?
Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.