11x11 Queens Puzzle #211
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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #211
What follows is a complete solve of puzzle #211, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 11 queen placements and 10 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 columns.
Techniques this board needs: last square in a region, region shadow, region confined to one line, pairing argument on rows, pairing argument on columns, last square in a row.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Only row 6, column 7 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 7, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. The orange region is down to one open square, at row 9, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 6, the remaining orange squares, and the ring of neighbours around row 9, column 6.
Step 3. Only row 11, column 2 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 2, in teal and in the ring around that square is now dead.
Step 4. Wherever indigo ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 5. Amber is down to 3 candidates in rows 1 and 2, columns 10 and 11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
The board after step 5 — 3 of 11 queens placed. Step 6. The slate region has 4 squares left, spread across rows 5, 7, and 8, columns 10 and 11. 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. Khaki cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 5 squares in all.
Step 8. Sea green is down to 3 candidates in rows 7, 8, and 10, columns 3 and 4, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about sea green itself.
Step 9. Indigo and amber are now boxed into rows 1 and 2 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 6 squares at once.
Step 10. Here is the pairing argument. The amber and slate regions have no open squares outside columns 10 and 11 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 6 squares come off in one stroke.
The board after step 10 — 3 of 11 queens placed. Step 11. Indigo and mint are now boxed into columns 8 and 9 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 6 squares at once.
Step 12. Row 10 has a single open square left, at column 4 in the sea green region. Every row needs a queen, so this one is forced. Cross out the whole of row 10 and column 4, the remaining sea green squares, and the ring of neighbours around row 10, column 4.
Step 13. Wherever blue 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 14. All of the pale yellow region's remaining squares (3 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.
Step 15. 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: row 5 is down to one square, putting a queen on row 5, column 11; amber has one square left, so its queen takes row 2, column 10; indigo has one square left, so its queen takes row 1, column 8; mint has one square left, so its queen takes row 4, column 9; blue has one square left, so its queen takes row 3, column 3; pale yellow has one square left, so its queen takes row 7, column 5; khaki has one square left, so its queen takes row 8, column 1. 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 8, column 1.
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 #211
11x11 puzzle #211 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.
As with every puzzle in this collection, #211 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 #211 are: red (1 square), teal (1 square), orange (3 squares), amber (4 squares), slate (6 squares), indigo (8 squares), khaki (8 squares), sea green (13 squares), mint (14 squares), blue (23 squares), pale yellow (40 squares). An even split would hand every color 11 squares, so the red region is running 10 squares under that average while the pale yellow region is the roomiest area on the grid with 40 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 pale yellow has 40 to spare, a gap of 39. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Amber is the densest region on this grid at 100% of a 2×2 frame; pale yellow is the loosest, occupying only 49% of its 9×9 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Below is every color on #211 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 covers 1 square, spanning 1 row and 1 column (rows 6–6, columns 7–7). It never leaves row 6, so its queen is locked to that row.
Teal occupies 1 square within rows 11–11, columns 2–2. It never leaves row 11, so its queen is locked to that row.
Orange: 3 squares across rows 8–9, columns 6–7.
Amber covers 4 squares, spanning 2 rows and 2 columns (rows 1–2, columns 10–11).
Slate occupies 6 squares within rows 5–8, columns 10–11.
Indigo: 8 squares across rows 1–3, columns 6–9.
Khaki covers 8 squares, spanning 6 rows and 2 columns (rows 6–11, columns 1–2).
Sea green occupies 13 squares within rows 7–11, columns 2–6.
Mint: 14 squares across rows 2–5, columns 7–11.
Blue covers 23 squares, spanning 6 rows and 5 columns (rows 1–6, columns 1–5).
Pale yellow occupies 40 squares within rows 3–11, columns 3–11.
Where to start on this board
The most constrained color is where a solve should begin, and on #211 that is red with 1 square. It reaches from row 6 to row 6 and from column 7 to column 7 — 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. Teal, amber and orange 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 #211
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 4 and 10 are the narrowest, touched by only 3 colors. Column 1 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 8, meeting 5 colors, is the opposite case — the busiest line on #211 and the last one you should expect to crack.
Working through the middle game
The middle of #211 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.
With eleven queens to seat and eleven regions competing over 121 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 11x11 boards quickly and players who stall halfway.
Resist the plausible-looking queen. On #211 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 #211 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 39. 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.
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.
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 1 on this board.
Here is a shape check that gives nothing away: when #211 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 #211?
Puzzle #211 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #211 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #211, 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 #211?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.