11x11 Queens Puzzle #65
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 14-step reasoning is written out below.
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Step-by-step solution for puzzle #65
What follows is a complete solve of puzzle #65, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 11 queen placements and 3 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: last square in a region, region shadow, region confined to one line, pairing argument on rows.
Show the full walkthrough (5 steps) — contains the solution
Step 1. Only row 10, column 11 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 11, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 2. Indigo is down to 3 candidates in rows 1 and 2, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
Step 3. Red cannot leave column 8 — 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: 9 squares in all.
The board after step 3 — 1 of 11 queens placed. Step 4. Here is the pairing argument. The indigo and amber regions have no open squares outside rows 1 and 2 — 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: 8 squares come off in one stroke.
Step 5. From here the board cascades. Keep alternating the region sweep and the line sweep and 10 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 2; indigo has one square left, so its queen takes row 1, column 1; mint has one square left, so its queen takes row 4, column 6; amber has one square left, so its queen takes row 2, column 9; pale yellow has one square left, so its queen takes row 7, column 3; slate has one square left, so its queen takes row 5, column 4; red has one square left, so its queen takes row 6, column 8; khaki has one square left, so its queen takes row 8, column 10; orange has one square left, so its queen takes row 9, column 5; teal has one square left, so its queen takes row 11, column 7. 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 7.
The board after step 5 — 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 #65
Puzzle #65 is one of the hard-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, #65 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 #65 are: sea green (1 square), indigo (3 squares), red (3 squares), blue (7 squares), mint (9 squares), amber (12 squares), pale yellow (12 squares), teal (12 squares), orange (19 squares), slate (20 squares), khaki (23 squares). An even split would hand every color 11 squares, so the sea green region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 23 squares.
Every color takes one queen and one only, whatever its size — which is why the 22 square difference between sea green and khaki 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.
Square count is only half the story — how a color is arranged counts too. Red is the tidiest shape on #65, packing 100% of its 3×1 bounding box, whereas mint straggles across its 3×6 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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.
Sea green occupies 1 square within rows 10–10, columns 11–11. It never leaves row 10, so its queen is locked to that row.
Indigo: 3 squares across rows 1–2, columns 1–2.
Red covers 3 squares, spanning 3 rows and 1 column (rows 5–7, columns 8–8). It sits wholly inside column 8, so its queen must be in that column.
Blue occupies 7 squares within rows 1–3, columns 2–5.
Mint: 9 squares across rows 2–4, columns 4–9.
Amber covers 12 squares, spanning 4 rows and 6 columns (rows 1–4, columns 6–11).
Pale yellow occupies 12 squares within rows 7–11, columns 1–3.
Teal: 12 squares across rows 9–11, columns 5–11.
Orange covers 19 squares, spanning 6 rows and 5 columns (rows 6–11, columns 3–7).
Slate occupies 20 squares within rows 3–6, columns 1–8.
Khaki: 23 squares across rows 2–10, columns 8–11.
Where to start on this board
Sea green is the natural opening on #65: it is the smallest region on the grid at 1 square, boxed into rows 10–10 and columns 11–11. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. 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. Indigo 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 #65
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 5, 8 and 11 are the narrowest, touched by only 3 colors. Columns 1 and 10 are the tightest columns, with 3 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 10 sits at the far end with 5 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.
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.
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 #65 is rated hard
Ratings track how generous the opening is. On #65 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 22-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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 #65 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 #65 is 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 #65?
Puzzle #65 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #65 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #65, 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 #65?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.