11x11 Queens Puzzle #184
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 13-step reasoning is written out below.
Previous puzzle · All 11x11 puzzles · Next puzzle
Step-by-step solution for puzzle #184
What follows is a complete solve of puzzle #184, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 11 queen placements and 2 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.
Show the full walkthrough (4 steps) — contains the solution
Step 1. Only row 2, column 4 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 4, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. Red is down to 4 candidates in rows 4–6, columns 5 and 6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about red itself.
The board after step 2 — 1 of 11 queens placed. Step 3. Indigo cannot leave row 1 — every one of its open squares (4 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 4 squares in all.
Step 4. From here the board cascades. Keep alternating the region sweep and the line sweep and 10 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 11; mint has one square left, so its queen takes row 4, column 3; slate has one square left, so its queen takes row 5, column 1; red has one square left, so its queen takes row 6, column 5; pale yellow has one square left, so its queen takes row 7, column 10; teal has one square left, so its queen takes row 11, column 6; khaki has one square left, so its queen takes row 8, column 8; sea green has one square left, so its queen takes row 10, column 9; indigo has one square left, so its queen takes row 1, column 7; orange has one square left, so its queen takes row 9, 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 9, column 2.
The board after step 4 — 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 #184
This is puzzle number 184 in the 11x11 collection, rated hard. The grid holds 121 squares split between eleven colored regions, and a finished board carries eleven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
Puzzle #184 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #184 are: amber (1 square), red (4 squares), blue (5 squares), teal (7 squares), pale yellow (8 squares), mint (10 squares), slate (10 squares), indigo (13 squares), sea green (17 squares), orange (19 squares), khaki (27 squares). An even split would hand every color 11 squares, so the amber region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 27 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Amber is working with 1 square while khaki has 27 to spare, a gap of 26. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here amber is the most solid, filling 100% of its 1×1 box, and khaki the most diffuse at 48% of its 8×7 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #184 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.
Amber covers 1 square, spanning 1 row and 1 column (rows 2–2, columns 4–4). It never leaves row 2, so its queen is locked to that row.
Red occupies 4 squares within rows 4–6, columns 5–6.
Blue: 5 squares across rows 1–3, columns 10–11.
Teal covers 7 squares, spanning 3 rows and 4 columns (rows 9–11, columns 3–6).
Pale yellow occupies 8 squares within rows 4–7, columns 10–11.
Mint: 10 squares across rows 1–4, columns 1–4.
Slate covers 10 squares, spanning 5 rows and 4 columns (rows 3–7, columns 1–4).
Indigo occupies 13 squares within rows 1–4, columns 4–9.
Sea green: 17 squares across rows 8–11, columns 6–11.
Orange covers 19 squares, spanning 6 rows and 5 columns (rows 6–11, columns 1–5).
Khaki occupies 27 squares within rows 2–9, columns 5–11.
Where to start on this board
Open on the tightest color. Here that is amber, confined to 1 square between rows 2 and 2 and columns 4 and 4. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #184.
Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: blue, red and pale yellow span only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
The tightest lines on puzzle #184
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 8, 10 and 11 are the narrowest, touched by only 3 colors. Columns 1, 2, 7, 8 and 9 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 4 is the crowded extreme at 6 colors — worth revisiting later, not now.
Working through the middle game
The middle of #184 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.
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 #184 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 26. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a hard board from the rest.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 1 on this board.
A non-spoiling distribution check: solved, #184 carries 4 queens on the perimeter against 7 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 11x11 Queens puzzle #184?
Puzzle #184 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #184 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #184, 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 #184?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.