11x11 Queens Puzzle #277
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.
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Step-by-step solution for puzzle #277
What follows is a complete solve of puzzle #277, 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 pairing argument on columns.
Techniques this board needs: region confined to one line, last square in a region, region shadow, pairing argument on rows, pairing argument on columns, last square in a column.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 9 squares in all.
Step 2. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 10 squares come off.
Step 3. Only row 3, column 1 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 1, in blue and in the ring around that square is now dead.
Step 4. The mint region is down to one open square, at row 4, column 11. Every colour holds exactly one queen, so that square is forced. Row 4 and column 11 are now spoken for, along with the squares touching that queen.
The board after step 4 — 2 of 11 queens placed. Step 5. Orange is down to 3 candidates in rows 9 and 10, columns 5 and 6, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about orange itself.
Step 6. The teal region has 3 squares left, spread across rows 10 and 11, columns 4 and 5. 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 7. Orange cannot leave row 9 — every one of its open squares (2 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 7 squares in all.
Step 8. Here is the pairing argument. The sea green and teal regions have no open squares outside rows 10 and 11 — 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 9. 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.
The board after step 9 — 2 of 11 queens placed. Step 10. Here is the pairing argument. The indigo, slate, khaki, and teal regions have no open squares outside columns 2–5 — 4 colours confined to 4 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.
Step 11. Only row 9, column 6 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 6, in orange and in the ring around that square is now dead.
Step 12. All of the red region's remaining squares (3 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 13. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: column 3 is down to one square, putting a queen on row 1, column 3; column 5 is down to one square, putting a queen on row 11, column 5; sea green has one square left, so its queen takes row 10, column 8; amber has one square left, so its queen takes row 2, column 9; red has one square left, so its queen takes row 6, column 7; pale yellow has one square left, so its queen takes row 7, column 10; slate has one square left, so its queen takes row 5, column 2; khaki has one square left, so its queen takes row 8, 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 8, column 4.
The board after step 13 — 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 #277
Puzzle #277 is one of the medium-rated boards in the 11x11 set. Eleven colors divide its 121 squares, and you win by placing eleven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
Like every board on this site, #277 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #277 are: indigo (3 squares), orange (3 squares), teal (3 squares), amber (4 squares), blue (7 squares), mint (7 squares), sea green (11 squares), khaki (15 squares), slate (18 squares), red (22 squares), pale yellow (28 squares). An even split would hand every color 11 squares, so the indigo region is running 8 squares under that average while the pale yellow region is the roomiest area on the grid with 28 squares.
Every color takes one queen and one only, whatever its size — which is why the 25 square difference between indigo and pale yellow is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×3 box that encloses it, while red is the most scattered at 45% of its 7×7 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
Region by region
Below is every color on #277 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.
Indigo covers 3 squares, spanning 1 row and 3 columns (rows 1–1, columns 3–5). It never leaves row 1, so its queen is locked to that row.
Orange occupies 3 squares within rows 9–10, columns 5–6.
Teal: 3 squares across rows 10–11, columns 4–5.
Amber covers 4 squares, spanning 2 rows and 2 columns (rows 1–2, columns 8–9).
Blue occupies 7 squares within rows 1–3, columns 1–4.
Mint: 7 squares across rows 1–4, columns 10–11.
Sea green covers 11 squares, spanning 3 rows and 6 columns (rows 9–11, columns 6–11).
Khaki occupies 15 squares within rows 8–11, columns 1–6.
Slate: 18 squares across rows 3–8, columns 1–4.
Red covers 22 squares, spanning 7 rows and 7 columns (rows 1–7, columns 3–9).
Pale yellow occupies 28 squares within rows 3–10, columns 7–11.
Where to start on this board
Indigo is the natural opening on #277: it is the smallest region on the grid at 3 squares, boxed into rows 1–1 and columns 3–5. Since one of those squares must hold a queen, that block of 1 row and 3 columns is the most contested part of the board.
Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Amber, orange and teal 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 #277
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5, 6, 7, 8 and 11 are the narrowest, touched by only 3 colors. Columns 1, 2, 7, 10 and 11 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 10 is the crowded extreme at 5 colors — worth revisiting later, not now.
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.
The whole middle game reduces to two sweeps. Sweep the eleven colors looking for one with a single square left; sweep the eleven rows and eleven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 11x11 solve from a stalled one.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #277 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers one single-line region, a 3-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 25. 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.
If #277 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #277 is row 5.
A non-spoiling distribution check: solved, #277 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 #277?
Puzzle #277 is rated medium. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #277 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #277, 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 #277?
Start with the indigo region — the most constrained color on this board, with 3 squares spanning rows 1–1 and columns 3–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.