11x11 Queens Puzzle #264
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #264
What follows is a complete solve of puzzle #264, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 11 queen placements and 8 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 columns, last square in a region, last square in a row.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 11 squares in all.
Step 2. Slate is down to 3 candidates in rows 5 and 6, columns 10 and 11, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about slate itself.
Step 3. The amber region has 4 squares left, spread across rows 2 and 3, columns 9–11. 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.
The board after step 3 — 0 of 11 queens placed. Step 4. Wherever pale yellow 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.
Step 5. Sea green cannot leave row 10 — every one of its open squares (2 open squares) sits there. That row belongs to sea green, so every square on it owned by another colour is dead: 13 squares in all.
Step 6. Here is the pairing argument. The amber, slate, red, and orange regions have no open squares outside columns 8–11 — 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: 10 squares come off in one stroke.
The board after step 6 — 0 of 11 queens placed. Step 7. Teal cannot leave row 11 — every one of its open squares (2 open squares) sits there. That row belongs to teal, so every square on it owned by another colour is dead: 3 squares in all.
Step 8. Here is the pairing argument. The pale yellow and teal regions have no open squares outside columns 6 and 7 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 10 squares come off in one stroke.
Step 9. From here the board cascades. Keep alternating the region sweep and the line sweep and 11 queens fall out in order without any new idea being needed: indigo has one square left, so its queen takes row 1, column 5; blue has one square left, so its queen takes row 3, column 4; amber has one square left, so its queen takes row 2, column 11; slate has one square left, so its queen takes row 5, column 10; mint has one square left, so its queen takes row 4, column 1; sea green has one square left, so its queen takes row 10, column 2; row 9 is down to one square, putting a queen on row 9, column 9; red has one square left, so its queen takes row 6, column 8; pale yellow has one square left, so its queen takes row 7, column 6; khaki has one square left, so its queen takes row 8, column 3; 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 9 — 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 #264
This is puzzle number 264 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.
There is exactly one way to finish #264, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these eleven regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #264 are: indigo (2 squares), sea green (2 squares), slate (3 squares), pale yellow (7 squares), amber (8 squares), orange (9 squares), red (10 squares), mint (12 squares), teal (12 squares), blue (17 squares), khaki (39 squares). An even split would hand every color 11 squares, so the indigo region is running 9 squares under that average while the khaki region is the roomiest area on the grid with 39 squares.
Every color takes one queen and one only, whatever its size — which is why the 37 square difference between indigo 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.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×2 box, and orange the most diffuse at 56% of its 4×4 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 #264, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo: 2 squares across rows 1–1, columns 5–6. It never leaves row 1, so its queen is locked to that row.
Sea green covers 2 squares, spanning 1 row and 2 columns (rows 10–10, columns 1–2). It never leaves row 10, so its queen is locked to that row.
Slate occupies 3 squares within rows 5–6, columns 10–11.
Pale yellow: 7 squares across rows 5–7, columns 6–8.
Amber covers 8 squares, spanning 4 rows and 3 columns (rows 1–4, columns 9–11).
Orange occupies 9 squares within rows 7–10, columns 8–11.
Red: 10 squares across rows 4–7, columns 7–10.
Mint covers 12 squares, spanning 5 rows and 4 columns (rows 1–5, columns 1–4).
Teal occupies 12 squares within rows 9–11, columns 6–11.
Blue: 17 squares across rows 1–4, columns 4–10.
Khaki covers 39 squares, spanning 8 rows and 7 columns (rows 4–11, columns 1–7).
Where to start on this board
Open on the tightest color. Here that is indigo, confined to 2 squares between rows 1 and 1 and columns 5 and 6. Its queen has nowhere else to go, which means those 1 row and 2 columns carry more constraint than anywhere else on #264.
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. Sea green and slate 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 #264
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 8 and 11 are the narrowest, touched by only 2 colors. Column 3 is the tightest column, with 2 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 5 is the crowded extreme at 5 colors — worth revisiting later, not now.
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 #264 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 #264 is rated medium
The rating reflects how much the board concedes up front. Puzzle #264 has two regions confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 37 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.
Stuck on #264 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 #264 is row 8.
A non-spoiling distribution check: solved, #264 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 #264?
Puzzle #264 is rated medium. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #264 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #264, 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 #264?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–1 and columns 5–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.