11x11 Queens Puzzle #280
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #280
What follows is a complete solve of puzzle #280, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 11 queen placements and 7 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, line confined to one region, last square in a column.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Only row 2, column 11 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 11, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. All of the mint region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 12 squares come off.
Step 3. The teal region has 4 squares left, spread across rows 10 and 11, columns 7–9. 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 4. Here is the pairing argument. The indigo and blue regions have no open squares outside rows 1 and 3 — 2 colours confined to 2 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.
The board after step 4 — 1 of 11 queens placed. Step 5. Only row 4, column 3 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 3, the rest of the mint region and every square adjacent to it — diagonals included.
Step 6. The slate region is down to one open square, at row 5, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 5, the remaining slate squares, and the ring of neighbours around row 5, column 5.
Step 7. Only row 6, column 7 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 7, in red and in the ring around that square is now dead.
Step 8. Pale yellow is down to 4 candidates in rows 7–9, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
The board after step 8 — 4 of 11 queens placed. Step 9. The khaki region has 2 squares left, spread across rows 7 and 8, columns 8 and 9. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
Step 10. All of the teal region's remaining squares (2 open squares) lie in row 11. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 11. Column 10 has only orange squares left (3 open squares). The column needs a queen and only orange can provide one, which pins that colour to this column and kills its squares elsewhere: 4 squares.
Step 12. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: column 6 is down to one square, putting a queen on row 1, column 6; blue has one square left, so its queen takes row 3, column 1; pale yellow has one square left, so its queen takes row 7, column 2; khaki has one square left, so its queen takes row 8, column 8; teal has one square left, so its queen takes row 11, column 9; orange has one square left, so its queen takes row 9, column 10; 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.
The board after step 12 — 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 #280
This is puzzle number 280 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 #280 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 #280 are: amber (1 square), mint (3 squares), teal (4 squares), blue (7 squares), slate (8 squares), khaki (8 squares), pale yellow (12 squares), red (14 squares), sea green (17 squares), indigo (20 squares), orange (27 squares). An even split would hand every color 11 squares, so the amber region is running 10 squares under that average while the orange 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 orange 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 53% of its 3×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
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.
Amber covers 1 square, spanning 1 row and 1 column (rows 2–2, columns 11–11). It never leaves row 2, so its queen is locked to that row.
Mint occupies 3 squares within rows 2–4, columns 3–3. It sits wholly inside column 3, so its queen must be in that column.
Teal: 4 squares across rows 10–11, columns 7–9.
Blue covers 7 squares, spanning 4 rows and 2 columns (rows 1–4, columns 1–2).
Slate occupies 8 squares within rows 3–5, columns 3–6.
Khaki: 8 squares across rows 6–8, columns 5–9.
Pale yellow covers 12 squares, spanning 6 rows and 3 columns (rows 4–9, columns 1–3).
Red occupies 14 squares within rows 3–6, columns 6–11.
Sea green: 17 squares across rows 6–11, columns 1–5.
Indigo covers 20 squares, spanning 3 rows and 9 columns (rows 1–3, columns 3–11).
Orange occupies 27 squares within rows 5–11, 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 11 and 11. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #280.
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.
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 #280
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Columns 1, 2, 4 and 10 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 6 is the crowded extreme at 5 colors — worth revisiting later, not now.
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.
Resist the plausible-looking queen. On #280 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #280 is rated hard
The hard label comes out of four measurable things about #280: three of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 26. Boards that score tight on those measures give up their first queen fast.
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, #280 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.
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Questions about this puzzle
How hard is 11x11 Queens puzzle #280?
Puzzle #280 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #280 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #280, 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 #280?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.