11x11 Queens Puzzle #203
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.
Previous puzzle · All 11x11 puzzles · Next puzzle
Step-by-step solution for puzzle #203
What follows is a complete solve of puzzle #203, 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 proof by contradiction.
Techniques this board needs: last square in a region, region confined to one line, pairing argument on rows, pairing argument on columns, proof by contradiction, region shadow, last square in a row.
Show the full walkthrough (12 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: red has one square left, so its queen takes row 6, column 4; teal has one square left, so its queen takes row 11, column 1; sea green has one square left, so its queen takes row 10, column 3; orange has one square left, so its queen takes row 9, 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 9, column 5.
Step 2. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 7 squares in all.
Step 3. All of the mint 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: 4 squares come off.
Step 4. Pale yellow cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 4 squares in all.
The board after step 4 — 4 of 11 queens placed. Step 5. Here is the pairing argument. The slate, pale yellow, and khaki regions have no open squares outside rows 5, 7, and 8 — 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 6. Mint cannot leave column 11 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 1 square in all.
Step 7. Here is the pairing argument. The indigo, amber, and khaki regions have no open squares outside columns 8–10 — 3 colours confined to 3 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 1 square come off in one stroke.
Step 8. Test row 1, column 9 for indigo: place a queen there, run the forced consequences through, and row 5 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
The board after step 8 — 4 of 11 queens placed. Step 9. The indigo region is down to one open square, at row 1, column 8. Every colour holds exactly one queen, so that square is forced. Row 1 and column 8 are now spoken for, along with the squares touching that queen.
Step 10. Test row 3, column 9 for amber: place a queen there, run the forced consequences through, and row 5 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 11. Amber is down to 2 candidates in rows 2 and 4, columns 9 and 10, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 12. 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: row 5 is down to one square, putting a queen on row 5, column 6; 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 11; amber has one square left, so its queen takes row 2, 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 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 7, column 2.
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 #203
11x11 puzzle #203 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.
Puzzle #203 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 #203 are: red (1 square), teal (1 square), indigo (2 squares), mint (4 squares), orange (10 squares), sea green (11 squares), amber (12 squares), blue (15 squares), pale yellow (20 squares), khaki (21 squares), slate (24 squares). An even split would hand every color 11 squares, so the red region is running 10 squares under that average while the slate region is the roomiest area on the grid with 24 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Red is working with 1 square while slate has 24 to spare, a gap of 23. 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 indigo is the most solid, filling 100% of its 1×2 box, and amber the most diffuse at 43% of its 7×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #203 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.
Red occupies 1 square within rows 6–6, columns 4–4. It never leaves row 6, so its queen is locked to that row.
Teal: 1 square across rows 11–11, columns 1–1. It never leaves row 11, so its queen is locked to that row.
Indigo covers 2 squares, spanning 1 row and 2 columns (rows 1–1, columns 8–9). It never leaves row 1, so its queen is locked to that row.
Mint occupies 4 squares within rows 3–6, columns 11–11. It sits wholly inside column 11, so its queen must be in that column.
Orange: 10 squares across rows 7–10, columns 3–7.
Sea green covers 11 squares, spanning 2 rows and 8 columns (rows 10–11, columns 1–8).
Amber occupies 12 squares within rows 1–7, columns 8–11.
Blue: 15 squares across rows 1–5, columns 5–9.
Pale yellow covers 20 squares, spanning 9 rows and 3 columns (rows 1–9, columns 1–3).
Khaki occupies 21 squares within rows 4–11, columns 8–11.
Slate: 24 squares across rows 1–9, columns 2–7.
Where to start on this board
The most constrained color is where a solve should begin, and on #203 that is red with 1 square. It reaches from row 6 to row 6 and from column 4 to column 4 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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, teal 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 #203
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 10 and 11 are the narrowest, touched by only 3 colors. Column 10 is the tightest column, with 2 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 6, meeting 6 colors, is the opposite case — the busiest line on #203 and the last one you should expect to crack.
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.
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 #203 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers six single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 23. 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 medium 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 column 10 on this board.
Here is a shape check that gives nothing away: when #203 is solved, 3 queens sit on the outer edge of the grid and 8 sit inside it, with 1 queen 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 11x11 Queens puzzle #203?
Puzzle #203 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and six of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #203 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #203, 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 #203?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.