11x11 Queens Puzzle #35
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #35
What follows is a complete solve of puzzle #35, 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 (13 steps) — contains the solution
Step 1. Only row 2, column 10 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 10, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. The teal region is down to one open square, at row 11, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 1, the remaining teal squares, and the ring of neighbours around row 11, column 1.
Step 3. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 10 squares in all.
Step 4. Wherever red ends up among its 7 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. Khaki cannot leave column 2 — 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: 7 squares in all.
Step 6. The red region has 3 squares left, spread across rows 6 and 7, columns 3 and 4. 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. Wherever sea green 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 8. The khaki region is down to one open square, at row 8, column 2. Every colour holds exactly one queen, so that square is forced. Row 8 and column 2 are now spoken for, along with the squares touching that queen.
Step 9. Red cannot leave column 4 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 5 squares in all.
The board after step 9 — 3 of 11 queens placed. Step 10. The sea green region is down to one open square, at row 10, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 3, the remaining sea green squares, and the ring of neighbours around row 10, column 3.
Step 11. Only row 3, column 5 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 5, in blue and in the ring around that square is now dead.
Step 12. The slate region has 3 squares left, spread across rows 5 and 6, columns 6 and 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 13. 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: pale yellow has one square left, so its queen takes row 7, column 6; slate has one square left, so its queen takes row 5, column 7; 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; red has one square left, so its queen takes row 6, column 4; orange has one square left, so its queen takes row 9, column 11. 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 11.
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 #35
11x11 puzzle #35 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.
Like every board on this site, #35 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 #35 are: amber (1 square), teal (1 square), khaki (7 squares), slate (8 squares), mint (9 squares), sea green (9 squares), red (12 squares), indigo (14 squares), blue (15 squares), pale yellow (16 squares), orange (29 squares). An even split would hand every color 11 squares, so the amber region is running 10 squares under that average while the orange region is the roomiest area on the grid with 29 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Amber has only 1 place to put its queen; orange has 29. The spread between them on this board is 28 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here amber is the most solid, filling 100% of its 1×1 box, and pale yellow the most diffuse at 38% of its 6×7 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #35 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.
Amber occupies 1 square within rows 2–2, columns 10–10. It never leaves row 2, 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.
Khaki covers 7 squares, spanning 5 rows and 2 columns (rows 6–10, columns 1–2).
Slate occupies 8 squares within rows 4–6, columns 3–7.
Mint: 9 squares across rows 2–5, columns 8–11.
Sea green covers 9 squares, spanning 4 rows and 4 columns (rows 8–11, columns 2–5).
Red occupies 12 squares within rows 2–8, columns 1–4.
Indigo: 14 squares across rows 1–4, columns 5–11.
Blue covers 15 squares, spanning 4 rows and 5 columns (rows 1–4, columns 1–5).
Pale yellow occupies 16 squares within rows 6–11, columns 4–10.
Orange: 29 squares across rows 4–11, columns 6–11.
Where to start on this board
The most constrained color is where a solve should begin, and on #35 that is amber with 1 square. It reaches from row 2 to row 2 and from column 10 to column 10 — 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 amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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 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 #35
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Column 11 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 2 colors, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 4 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.
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 #35 is rated hard
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 2 colors, and a region-size spread of 28. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
If #35 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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #35 the place to look for one is around row 1.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 8 queens in the middle, including 1 in a corner. 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 #35?
Puzzle #35 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #35 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #35, 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 #35?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 10–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.