11x11 Queens Puzzle #206
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 18-step reasoning is written out below.
Previous puzzle · All 11x11 puzzles · Next puzzle
Step-by-step solution for puzzle #206
What follows is a complete solve of puzzle #206, 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 region shadow.
Techniques this board needs: last square in a region, region confined to one line, region shadow.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Only row 6, column 8 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 8, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. The sea green region is down to one open square, at row 10, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 10, the remaining sea green squares, and the ring of neighbours around row 10, column 10.
Step 3. 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 4. Wherever amber 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.
The board after step 4 — 2 of 11 queens placed. Step 5. Blue is down to 3 candidates in rows 2 and 3, columns 3 and 5, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 6. The khaki region has 5 squares left, spread across rows 7–9, columns 5–7. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 7. Orange cannot leave column 1 — 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: 6 squares in all.
Step 8. The amber region is down to one open square, at row 2, column 2. Every colour holds exactly one queen, so that square is forced. Row 2 and column 2 are now spoken for, along with the squares touching that queen.
The board after step 8 — 3 of 11 queens placed. Step 9. Only row 3, column 5 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 5, the rest of the blue region and every square adjacent to it — diagonals included.
Step 10. Wherever mint 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.
Step 11. Khaki cannot leave row 8 — every one of its open squares (2 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 6 squares in all.
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: pale yellow has one square left, so its queen takes row 7, column 11; indigo has one square left, so its queen takes row 1, column 9; 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 6; khaki has one square left, so its queen takes row 8, column 7; orange has one square left, so its queen takes row 9, column 1; teal has one square left, so its queen takes row 11, 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 11, 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 #206
Board #206 of the 11x11 bank carries a medium 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.
As with every puzzle in this collection, #206 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #206 are: red (1 square), sea green (1 square), amber (5 squares), orange (5 squares), indigo (6 squares), khaki (6 squares), blue (8 squares), mint (16 squares), pale yellow (17 squares), slate (28 squares), teal (28 squares). An even split would hand every color 11 squares, so the red region is running 10 squares under that average while the teal region is the roomiest area on the grid with 28 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 red, with 1 square, is under far more pressure than teal with 28. A 27-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. Red is the tidiest shape on #206, packing 100% of its 1×1 bounding box, whereas khaki straggles across its 4×3 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 medium board.
Red occupies 1 square within rows 6–6, columns 8–8. It never leaves row 6, so its queen is locked to that row.
Sea green: 1 square across rows 10–10, columns 10–10. It never leaves row 10, so its queen is locked to that row.
Amber covers 5 squares, spanning 3 rows and 2 columns (rows 1–3, columns 1–2).
Orange occupies 5 squares within rows 6–10, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Indigo: 6 squares across rows 1–3, columns 8–11.
Khaki covers 6 squares, spanning 4 rows and 3 columns (rows 6–9, columns 5–7).
Blue occupies 8 squares within rows 1–3, columns 3–7.
Mint: 16 squares across rows 2–7, columns 1–5.
Pale yellow covers 17 squares, spanning 5 rows and 5 columns (rows 6–10, columns 7–11).
Slate occupies 28 squares within rows 2–7, columns 3–11.
Teal: 28 squares across rows 7–11, columns 1–11.
Where to start on this board
Begin where the choices are fewest. On this board that means red, which owns just 1 square inside a 1×1 window running from row 6 to row 6 and column 8 to column 8. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
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. Sea green 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 #206
A quick way to find the next move is to count how many different colors touch each line. On this board, row 11 is the narrowest, touched by only 1 color. Column 2 is the tightest column, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 1 color, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 7 sits at the far end with 6 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
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.
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 #206 is rated medium
The medium label comes out of four measurable things about #206: five of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 1 color, and its largest and smallest regions differ by 27. Boards that score tight on those measures give up their first queen fast.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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 #206, start hunting for it near row 11.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 7 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #206?
Puzzle #206 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 1 color, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #206 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #206, 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 #206?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.