11x11 Queens Puzzle #271
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 22-step reasoning is written out below.
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Step-by-step solution for puzzle #271
What follows is a complete solve of puzzle #271, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 11 queen placements and 11 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: region confined to one line, last square in a region, pairing argument on rows, region shadow, last square in a row.
Show the full walkthrough (22 steps) — contains the solution
Step 1. Indigo cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to indigo, so every square in it owned by another colour is dead: 13 squares in all.
Step 2. The blue region is down to one open square, at row 3, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 4, the remaining blue squares, and the ring of neighbours around row 3, column 4.
Step 3. Only row 1, column 5 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 5, in indigo and in the ring around that square is now dead.
Step 4. All of the amber region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 5. Slate cannot leave column 1 — every one of its open squares (3 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 6 squares in all.
Step 6. All of the red region's remaining squares (4 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
The board after step 6 — 2 of 11 queens placed. Step 7. Sea green cannot leave column 11 — every one of its open squares (4 open squares) sits there. That column belongs to sea green, so every square in it owned by another colour is dead: 5 squares in all.
Step 8. All of the khaki region's remaining squares (6 open squares) lie in column 10. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 9. Only row 9, column 8 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 8, the rest of the orange region and every square adjacent to it — diagonals included.
Step 10. All of the mint region's remaining squares (2 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
Step 11. Red cannot leave column 9 — every one of its open squares (3 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 1 square in all.
The board after step 11 — 3 of 11 queens placed. Step 12. Here is the pairing argument. The amber and mint regions have no open squares outside rows 2 and 4 — 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.
Step 13. Only row 5, column 1 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 1, the rest of the slate region and every square adjacent to it — diagonals included.
Step 14. 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. Cross out the whole of row 2 and column 2, the remaining amber squares, and the ring of neighbours around row 2, column 2.
Step 15. Only row 4, column 7 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 7, in mint and in the ring around that square is now dead.
Step 16. All of the red region's remaining squares (2 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.
Step 17. Only row 8, column 10 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 10, the rest of the khaki region and every square adjacent to it — diagonals included.
The board after step 17 — 7 of 11 queens placed. Step 18. The red region is down to one open square, at row 6, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 9, the remaining red squares, and the ring of neighbours around row 6, column 9.
Step 19. Wherever pale yellow ends up among its 2 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 20. Row 7 has a single open square left, at column 6 in the pale yellow region. Every row needs a queen, so this one is forced. Cross out the whole of row 7 and column 6, the remaining pale yellow squares, and the ring of neighbours around row 7, column 6.
Step 21. Only row 11, column 3 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 3, the rest of the teal region and every square adjacent to it — diagonals included.
Step 22. The sea green region is down to one open square, at row 10, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 11, the remaining sea green squares, and the ring of neighbours around row 10, column 11.
The board after step 22 — 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 #271
11x11 puzzle #271 is rated hard. 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 #271 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 #271 are: indigo (2 squares), blue (3 squares), red (4 squares), sea green (4 squares), amber (7 squares), slate (7 squares), orange (7 squares), mint (15 squares), khaki (18 squares), teal (25 squares), pale yellow (29 squares). An even split would hand every color 11 squares, so the indigo region is running 9 squares under that average while the pale yellow region is the roomiest area on the grid with 29 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Indigo is working with 2 squares while pale yellow has 29 to spare, a gap of 27. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 2×1 frame; mint is the loosest, occupying only 50% of its 6×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Indigo covers 2 squares, spanning 2 rows and 1 column (rows 1–2, columns 5–5). It sits wholly inside column 5, so its queen must be in that column.
Blue occupies 3 squares within rows 1–3, columns 4–4. It sits wholly inside column 4, so its queen must be in that column.
Red: 4 squares across rows 5–8, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.
Sea green covers 4 squares, spanning 4 rows and 1 column (rows 8–11, columns 11–11). It sits wholly inside column 11, so its queen must be in that column.
Amber occupies 7 squares within rows 1–4, columns 2–3.
Slate: 7 squares across rows 1–6, columns 1–2.
Orange covers 7 squares, spanning 3 rows and 3 columns (rows 9–11, columns 8–10).
Mint occupies 15 squares within rows 1–6, columns 5–9.
Khaki: 18 squares across rows 1–8, columns 9–11.
Teal covers 25 squares, spanning 6 rows and 8 columns (rows 6–11, columns 1–8).
Pale yellow occupies 29 squares within rows 4–10, columns 3–8.
Where to start on this board
The most constrained color is where a solve should begin, and on #271 that is indigo with 2 squares. It reaches from row 1 to row 2 and from column 5 to column 5 — 2 rows 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 indigo stays inside column 5, its queen belongs to that column and no other region may use it. Cross out the rest of column 5 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: slate and amber 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 #271
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 3 colors. Columns 1, 10 and 11 are the tightest columns, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 6 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
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
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 #271 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 #271 is rated hard
Ratings track how generous the opening is. On #271 you get four regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 3 colors, and a 27-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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 column 1 on this board.
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.
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Questions about this puzzle
How hard is 11x11 Queens puzzle #271?
Puzzle #271 is rated hard. Its smallest color region holds 2 squares, 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 #271 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #271, 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 #271?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–2 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.