11x11 Queens Puzzle #267
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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #267
What follows is a complete solve of puzzle #267, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 11 queen placements and 10 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: region shadow, pairing argument on rows, last square in a region, region confined to one line, last square in a column.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Wherever indigo 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 2. Orange is down to 5 candidates in rows 8–10, columns 7 and 8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about orange itself.
Step 3. 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 4. 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: 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 9; teal has one square left, so its queen takes row 11, column 10. 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 10.
The board after step 4 — 4 of 11 queens placed. Step 5. All of the pale yellow region's remaining squares (3 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 6. Only row 4, column 8 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 8, the rest of the mint region and every square adjacent to it — diagonals included.
Step 7. Wherever slate ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Orange cannot leave column 7 — every one of its open squares (3 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 3 squares in all.
Step 9. All of the sea green region's remaining squares (2 open squares) lie in row 10. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
The board after step 9 — 5 of 11 queens placed. Step 10. Orange cannot leave column 7 — every one of its open squares (2 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 1 square in all.
Step 11. Here is the pairing argument. The pale yellow, khaki, and orange regions have no open squares outside rows 7–9 — 3 colours confined to 3 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 12. The red region has 3 squares left, spread across rows 5 and 6, columns 5 and 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.
Step 13. 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: column 4 is down to one square, putting a queen on row 8, column 4; orange has one square left, so its queen takes row 9, column 7; pale yellow has one square left, so its queen takes row 7, column 11; column 6 is down to one square, putting a queen on row 6, column 6; 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 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.
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 #267
11x11 puzzle #267 is rated medium. Eleven colored regions cover its 121 squares, and your job is to seat eleven queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Like every board on this site, #267 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 #267 are: indigo (3 squares), orange (5 squares), teal (6 squares), amber (7 squares), blue (10 squares), sea green (12 squares), pale yellow (13 squares), red (14 squares), mint (16 squares), khaki (16 squares), slate (19 squares). An even split would hand every color 11 squares, so the indigo region is running 8 squares under that average while the slate region is the roomiest area on the grid with 19 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 3 places to put its queen; slate has 19. The spread between them on this board is 16 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 orange is the most solid, filling 83% of its 3×2 box, and khaki the most diffuse at 40% of its 5×8 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #267 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Indigo: 3 squares across rows 1–2, columns 1–2.
Orange covers 5 squares, spanning 3 rows and 2 columns (rows 8–10, columns 7–8).
Teal occupies 6 squares within rows 8–11, columns 8–10.
Amber: 7 squares across rows 1–2, columns 6–11.
Blue covers 10 squares, spanning 3 rows and 6 columns (rows 1–3, columns 2–7).
Sea green occupies 12 squares within rows 10–11, columns 1–8.
Pale yellow: 13 squares across rows 5–11, columns 9–11.
Red covers 14 squares, spanning 5 rows and 7 columns (rows 4–8, columns 3–9).
Mint occupies 16 squares within rows 2–6, columns 5–11.
Khaki: 16 squares across rows 6–10, columns 1–8.
Slate covers 19 squares, spanning 5 rows and 6 columns (rows 3–7, columns 1–6).
Where to start on this board
The most constrained color is where a solve should begin, and on #267 that is indigo with 3 squares. It reaches from row 1 to row 2 and from column 1 to column 2 — 2 rows by 2 columns. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Indigo spans 2 rows, so it stays open for now — but it is still the shortest list on the board at 3 squares. Work through those squares first and mark the ones that would leave another region homeless. That pruning is what makes the rest of the grid legible.
Work outward to the other flat regions next. Amber and sea green 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 #267
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3, 4 and 11 are the narrowest, touched by only 3 colors. Column 11 is the tightest column, 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 10 rows. By contrast row 10 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
The middle of #267 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
With eleven queens to seat and eleven regions competing over 121 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 11x11 boards quickly and players who stall halfway.
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 #267 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers no single-line region at all, a 3-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 16. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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 #267 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 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.
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 #267 the place to look for one is around row 1.
As a sanity check rather than a spoiler: the finished solution to #267 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 #267?
Puzzle #267 is rated medium. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 11x11 puzzle #267 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #267, 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 #267?
Start with the indigo region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.