11x11 Queens Puzzle #7
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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #7
What follows is a complete solve of puzzle #7, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 11 queen placements and 6 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 line confined to one region.
Techniques this board needs: last square in a region, region shadow, region confined to one line, line confined to one region, last square in a column.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Only row 6, column 1 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 1, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. The teal region is down to one open square, at row 11, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 5, the remaining teal squares, and the ring of neighbours around row 11, column 5.
Step 3. Only row 10, column 10 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 10, in sea green and in the ring around that square is now dead.
Step 4. Wherever blue ends up among its 4 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 — 3 of 11 queens placed. Step 5. Slate cannot leave column 11 — every one of its open squares (4 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 3 squares in all.
Step 6. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 7 squares come off.
Step 7. Only row 3, column 2 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 2, in blue and in the ring around that square is now dead.
Step 8. All of the mint region's remaining squares (2 open squares) lie in column 4. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
The board after step 8 — 4 of 11 queens placed. Step 9. Pale yellow cannot leave column 3 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 2 squares in all.
Step 10. 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 11. Row 8 has only khaki squares left (2 open squares). The row needs a queen and only khaki can provide one, which pins that colour to this row and kills its squares elsewhere: 5 squares.
Step 12. 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: column 7 is down to one square, putting a queen on row 2, column 7; indigo has one square left, so its queen takes row 1, column 9; mint has one square left, so its queen takes row 4, column 4; 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 11; khaki has one square left, so its queen takes row 8, column 8. 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 8.
The board after step 12 — 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 #7
11x11 puzzle #7 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, #7 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 #7 are: red (1 square), teal (1 square), sea green (3 squares), indigo (6 squares), blue (10 squares), slate (11 squares), amber (13 squares), pale yellow (15 squares), mint (18 squares), khaki (18 squares), orange (25 squares). An even split would hand every color 11 squares, so the red region is running 10 squares under that average while the orange region is the roomiest area on the grid with 25 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Red has only 1 place to put its queen; orange has 25. The spread between them on this board is 24 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Red is the densest region on this grid at 100% of a 1×1 frame; mint is the loosest, occupying only 45% of its 8×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Here is the full footprint of every color on puzzle #7, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Red covers 1 square, spanning 1 row and 1 column (rows 6–6, columns 1–1). It never leaves row 6, so its queen is locked to that row.
Teal occupies 1 square within rows 11–11, columns 5–5. It never leaves row 11, so its queen is locked to that row.
Sea green: 3 squares across rows 10–11, columns 10–11.
Indigo covers 6 squares, spanning 2 rows and 4 columns (rows 1–2, columns 8–11).
Blue occupies 10 squares within rows 1–5, columns 1–4.
Slate: 11 squares across rows 3–7, columns 9–11.
Amber covers 13 squares, spanning 5 rows and 4 columns (rows 1–5, columns 6–9).
Pale yellow occupies 15 squares within rows 5–11, columns 1–4.
Mint: 18 squares across rows 1–8, columns 2–6.
Khaki covers 18 squares, spanning 6 rows and 5 columns (rows 4–9, columns 6–10).
Orange occupies 25 squares within rows 8–11, columns 2–11.
Where to start on this board
The most constrained color is where a solve should begin, and on #7 that is red with 1 square. It reaches from row 6 to row 6 and from column 1 to column 1 — 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, indigo and sea green 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 #7
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 9 and 10 are the narrowest, touched by only 3 colors. Columns 1, 5 and 7 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 5 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
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
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 #7 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 #7 is rated hard
The rating reflects how much the board concedes up front. Puzzle #7 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 24 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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 #7 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 #7 the place to look for one is around row 9.
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 #7?
Puzzle #7 is rated hard. 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 #7 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #7, 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 #7?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.