11x11 Queens Puzzle #72
Difficulty: easy. 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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #72
What follows is a complete solve of puzzle #72, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 11 queen placements and 4 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 confined to one line, region shadow, pairing argument on rows.
Show the full walkthrough (6 steps) — contains the solution
Step 1. Only row 2, column 1 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 1, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (3 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 3. 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: 10 squares in all.
The board after step 3 — 1 of 11 queens placed. Step 4. Wherever sea green ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Orange and sea green are now boxed into rows 9 and 10 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 8 squares at once.
Step 6. 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: khaki has one square left, so its queen takes row 8, column 5; pale yellow has one square left, so its queen takes row 7, column 11; red has one square left, so its queen takes row 6, column 2; slate has one square left, so its queen takes row 5, column 9; sea green has one square left, so its queen takes row 10, column 3; teal has one square left, so its queen takes row 11, column 8; blue has one square left, so its queen takes row 3, column 10; orange has one square left, so its queen takes row 9, column 7; indigo has one square left, so its queen takes row 1, column 6; mint has one square left, so its queen takes row 4, column 4. 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 4, column 4.
The board after step 6 — 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 #72
This is puzzle number 72 in the 11x11 collection, rated easy. 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.
Puzzle #72 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #72 are: amber (1 square), teal (2 squares), indigo (7 squares), khaki (7 squares), red (8 squares), sea green (8 squares), pale yellow (9 squares), orange (10 squares), slate (11 squares), blue (19 squares), mint (39 squares). An even split would hand every color 11 squares, so the amber region is running 10 squares under that average while the mint region is the roomiest area on the grid with 39 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Amber is working with 1 square while mint has 39 to spare, a gap of 38. Attack the cramped end and the roomy regions tend to resolve themselves.
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 red the most diffuse at 50% of its 4×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a easy board.
Amber: 1 square across rows 2–2, columns 1–1. It never leaves row 2, so its queen is locked to that row.
Teal covers 2 squares, spanning 1 row and 2 columns (rows 11–11, columns 8–9). It never leaves row 11, so its queen is locked to that row.
Indigo occupies 7 squares within rows 1–2, columns 5–8.
Khaki: 7 squares across rows 8–11, columns 3–5.
Red covers 8 squares, spanning 4 rows and 4 columns (rows 6–9, columns 1–4).
Sea green occupies 8 squares within rows 9–11, columns 1–4.
Pale yellow: 9 squares across rows 7–11, columns 10–11.
Orange covers 10 squares, spanning 3 rows and 4 columns (rows 9–11, columns 6–9).
Slate occupies 11 squares within rows 5–8, columns 7–11.
Blue: 19 squares across rows 1–6, columns 8–11.
Mint covers 39 squares, spanning 8 rows and 7 columns (rows 1–8, columns 1–7).
Where to start on this board
Open on the tightest color. Here that is amber, confined to 1 square between rows 2 and 2 and columns 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #72.
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 and indigo 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 #72
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3 and 4 are the narrowest, touched by only 2 colors. Columns 2, 5, 6, 10 and 11 are the tightest columns, with 3 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 11 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
The middle of #72 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
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 #72 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 #72 is rated easy
The easy label comes out of four measurable things about #72: three of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 38. Boards that score tight on those measures give up their first queen fast.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a easy board from the rest.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 3 on this board.
A non-spoiling distribution check: solved, #72 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 #72?
Puzzle #72 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #72 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #72, 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 #72?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.