11x11 Queens Puzzle #8
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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #8
What follows is a complete solve of puzzle #8, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 11 queen placements and 10 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, region shadow, pairing argument on rows, pairing argument on columns, last square in a region, last square in a column.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Teal cannot leave row 11 — every one of its open squares (3 open squares) sits there. That row belongs to teal, so every square on it owned by another colour is dead: 9 squares in all.
Step 2. All of the sea green region's remaining squares (2 open squares) lie in row 10. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 10 squares come off.
Step 3. Orange cannot leave row 9 — every one of its open squares (3 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 4. Wherever pale yellow ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Pale yellow and khaki are now boxed into rows 7 and 8 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 11 squares at once.
The board after step 5 — 0 of 11 queens placed. Step 6. Here is the pairing argument. The blue, orange, and teal regions have no open squares outside columns 1–3 — 3 colours confined to 3 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 16 squares come off in one stroke.
Step 7. Red cannot leave row 6 — every one of its open squares (2 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 9 squares in all.
Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: khaki has one square left, so its queen takes row 8, column 4; red has one square left, so its queen takes row 6, column 5; pale yellow has one square left, so its queen takes row 7, column 10; sea green has one square left, so its queen takes row 10, column 11; amber has one square left, so its queen takes row 2, column 9; column 3 is down to one square, putting a queen on row 11, column 3; column 2 is down to one square, putting a queen on row 9, column 2. 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 2.
Step 9. The mint region has 4 squares left, spread across rows 3 and 4, columns 6–8. 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 10. 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: 1 square come off.
The board after step 10 — 7 of 11 queens placed. Step 11. Only row 3, column 1 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 1, the rest of the blue region and every square adjacent to it — diagonals included.
Step 12. All of the mint region's remaining squares (3 open squares) lie in row 4. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 13. Only row 5, column 8 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 8, in slate and in the ring around that square is now dead.
Step 14. The mint region is down to one open square, at row 4, column 6. Every colour holds exactly one queen, so that square is forced. Row 4 and column 6 are now spoken for, along with the squares touching that queen.
Step 15. Only row 1, column 7 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 7, the rest of the indigo region and every square adjacent to it — diagonals included.
The board after step 15 — 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 #8
This is puzzle number 8 in the 11x11 collection, rated medium. The grid holds 121 squares split between eleven colored regions, and a finished board carries eleven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
As with every puzzle in this collection, #8 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #8 are: teal (3 squares), blue (4 squares), sea green (7 squares), amber (8 squares), khaki (9 squares), orange (11 squares), pale yellow (12 squares), indigo (13 squares), mint (16 squares), slate (18 squares), red (20 squares). An even split would hand every color 11 squares, so the teal region is running 8 squares under that average while the red region is the roomiest area on the grid with 20 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Teal has only 3 places to put its queen; red has 20. The spread between them on this board is 17 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 teal is the most solid, filling 100% of its 1×3 box, and khaki the most diffuse at 45% of its 4×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Here is the full footprint of every color on puzzle #8, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Teal occupies 3 squares within rows 11–11, columns 1–3. It never leaves row 11, so its queen is locked to that row.
Blue: 4 squares across rows 1–3, columns 1–2.
Sea green covers 7 squares, spanning 2 rows and 5 columns (rows 10–11, columns 7–11).
Amber occupies 8 squares within rows 1–4, columns 9–11.
Khaki: 9 squares across rows 7–10, columns 3–7.
Orange covers 11 squares, spanning 3 rows and 6 columns (rows 9–11, columns 1–6).
Pale yellow occupies 12 squares within rows 7–10, columns 7–11.
Indigo: 13 squares across rows 1–3, columns 5–10.
Mint covers 16 squares, spanning 5 rows and 7 columns (rows 1–5, columns 2–8).
Slate occupies 18 squares within rows 4–8, columns 6–11.
Red: 20 squares across rows 3–8, columns 1–6.
Where to start on this board
Open on the tightest color. Here that is teal, confined to 3 squares between rows 11 and 11 and columns 1 and 3. Its queen has nowhere else to go, which means those 1 row and 3 columns carry more constraint than anywhere else on #8.
Because teal never leaves row 11, its queen must be in that row — and that instantly settles row 11 for everyone else. Sweep along it and X out every square that is not teal. 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. Sea green 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 #8
A quick way to find the next move is to count how many different colors touch each line. On this board, row 6 is the narrowest, touched by only 2 colors. Columns 1, 4 and 11 are the tightest columns, with 4 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 3 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
Resist the plausible-looking queen. On #8 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 #8 is rated medium
The rating reflects how much the board concedes up front. Puzzle #8 has one region confined to a single row or column, its smallest color holds 3 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 17 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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 #8 the place to look for one is around row 6.
As a sanity check rather than a spoiler: the finished solution to #8 puts 4 queens on the outer border and 7 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #8?
Puzzle #8 is rated medium. Its smallest color region holds 3 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #8 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #8, 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 #8?
Start with the teal region — the most constrained color on this board, with 3 squares spanning rows 11–11 and columns 1–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.