11x11 Queens Puzzle #182
Difficulty: hard. 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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #182
What follows is a complete solve of puzzle #182, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 11 queen placements and 8 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 shadow, region confined to one line, pairing argument on rows.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Only row 9, column 9 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 9, the rest of the orange region and every square adjacent to it — diagonals included.
Step 2. Mint is down to 5 candidates in rows 3–5, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 3. Slate cannot leave column 11 — every one of its open squares (2 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 10 squares in all.
Step 4. The teal region is down to one open square, at row 11, column 10. Every colour holds exactly one queen, so that square is forced. Row 11 and column 10 are now spoken for, along with the squares touching that queen.
Step 5. Red cannot leave row 6 — every one of its open squares (2 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 11 squares in all.
The board after step 5 — 2 of 11 queens placed. Step 6. The slate region is down to one open square, at row 5, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 11, the remaining slate squares, and the ring of neighbours around row 5, column 11.
Step 7. Wherever mint 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 8. 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: 5 squares come off.
Step 9. Indigo, amber, blue, and mint are now boxed into rows 1–4 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 3 squares at once.
Step 10. Wherever pale yellow ends up among its 2 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
The board after step 10 — 3 of 11 queens placed. Step 11. 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: red has one square left, so its queen takes row 6, column 8; blue has one square left, so its queen takes row 3, column 7; mint has one square left, so its queen takes row 4, column 1; pale yellow has one square left, so its queen takes row 7, column 6; sea green has one square left, so its queen takes row 10, column 2. 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 2.
Step 12. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
Step 13. Only row 2, column 3 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 3, the rest of the amber region and every square adjacent to it — diagonals included.
Step 14. The indigo region is down to one open square, at row 1, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 5, the remaining indigo squares, and the ring of neighbours around row 1, column 5.
Step 15. Only row 8, column 4 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 4, in khaki and in the ring around that square is now dead.
The board after step 15 — 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 #182
Board #182 of the 11x11 bank carries a hard rating. Its 121 squares are shared between eleven colored regions, and the solution places eleven queens: one per row, one per column, one per region, none of them side by side or corner to corner.
Like every board on this site, #182 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 #182 are: orange (1 square), slate (2 squares), mint (5 squares), indigo (7 squares), sea green (10 squares), red (11 squares), teal (12 squares), pale yellow (17 squares), amber (18 squares), blue (19 squares), khaki (19 squares). An even split would hand every color 11 squares, so the orange region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 19 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 orange, with 1 square, is under far more pressure than khaki with 19. A 18-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. Slate is the tidiest shape on #182, packing 100% of its 2×1 bounding box, whereas amber straggles across its 6×6 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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.
Orange occupies 1 square within rows 9–9, columns 9–9. It never leaves row 9, so its queen is locked to that row.
Slate: 2 squares across rows 5–6, columns 11–11. It sits wholly inside column 11, so its queen must be in that column.
Mint covers 5 squares, spanning 3 rows and 2 columns (rows 3–5, columns 1–2).
Indigo occupies 7 squares within rows 1–2, columns 4–8.
Sea green: 10 squares across rows 9–11, columns 1–6.
Red covers 11 squares, spanning 4 rows and 5 columns (rows 5–8, columns 7–11).
Teal occupies 12 squares within rows 8–11, columns 8–11.
Pale yellow: 17 squares across rows 4–11, columns 5–8.
Amber covers 18 squares, spanning 6 rows and 6 columns (rows 1–6, columns 1–6).
Blue occupies 19 squares within rows 1–5, columns 6–11.
Khaki: 19 squares across rows 6–10, columns 1–6.
Where to start on this board
Begin where the choices are fewest. On this board that means orange, which owns just 1 square inside a 1×1 window running from row 9 to row 9 and column 9 to column 9. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. 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 slate 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 #182
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 7 and 11 are the narrowest, touched by only 3 colors. Columns 3 and 10 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 5, meeting 6 colors, is the opposite case — the busiest line on #182 and the last one you should expect to crack.
Working through the middle game
The middle of #182 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.
Keep alternating between two views of the board. In the region view you ask which of the eleven 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 11x11 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 #182 is rated hard
The hard label comes out of four measurable things about #182: 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 18. Boards that score tight on those measures give up their first queen fast.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
If #182 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.
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 #182, start hunting for it near row 1.
Here is a shape check that gives nothing away: when #182 is solved, 4 queens sit on the outer edge of the grid and 7 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #182?
Puzzle #182 is rated hard. 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 #182 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #182, 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 #182?
Start with the orange region — the most constrained color on this board, with 1 square spanning rows 9–9 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.