11x11 Queens Puzzle #252
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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #252
What follows is a complete solve of puzzle #252, 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 shadow, pairing argument on rows, region confined to one line.
Show the full walkthrough (7 steps) — contains the solution
Step 1. Only row 1, column 3 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 3, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. Slate is down to 6 candidates in rows 2–5, columns 2, 4, 5, and 6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
Step 3. Amber, blue, mint, and slate are now boxed into rows 2–5 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 13 squares at once.
Step 4. All of the red region's remaining squares (3 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.
The board after step 4 — 1 of 11 queens placed. Step 5. 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: pale yellow has one square left, so its queen takes row 7, column 11; sea green has one square left, so its queen takes row 10, column 10; amber has one square left, so its queen takes row 2, column 9; blue has one square left, so its queen takes row 3, column 7; orange has one square left, so its queen takes row 9, column 8; red has one square left, so its queen takes row 6, column 6. 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 6, column 6.
Step 6. Mint cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 3 squares in all.
Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: slate has one square left, so its queen takes row 5, column 4; mint has one square left, so its queen takes row 4, column 1; teal has one square left, so its queen takes row 11, column 5; khaki has one square left, so its queen takes row 8, 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 8, column 2.
The board after step 7 — 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 #252
This is puzzle number 252 in the 11x11 collection, rated hard. 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 #252 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 #252 are: indigo (1 square), mint (6 squares), pale yellow (7 squares), sea green (7 squares), amber (10 squares), teal (10 squares), blue (11 squares), slate (13 squares), red (13 squares), orange (13 squares), khaki (30 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 30 squares.
Every color takes one queen and one only, whatever its size — which is why the 29 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 1×1 box, and blue the most diffuse at 39% of its 4×7 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #252 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Indigo: 1 square across rows 1–1, columns 3–3. It never leaves row 1, so its queen is locked to that row.
Mint covers 6 squares, spanning 5 rows and 2 columns (rows 1–5, columns 1–2).
Pale yellow occupies 7 squares within rows 4–7, columns 9–11.
Sea green: 7 squares across rows 7–11, columns 10–11.
Amber covers 10 squares, spanning 3 rows and 5 columns (rows 1–3, columns 7–11).
Teal occupies 10 squares within rows 9–11, columns 3–8.
Blue: 11 squares across rows 1–4, columns 4–10.
Slate covers 13 squares, spanning 5 rows and 5 columns (rows 1–5, columns 2–6).
Red occupies 13 squares within rows 4–6, columns 4–9.
Orange: 13 squares across rows 7–11, columns 7–10.
Khaki covers 30 squares, spanning 7 rows and 8 columns (rows 5–11, columns 1–8).
Where to start on this board
Open on the tightest color. Here that is indigo, confined to 1 square between rows 1 and 1 and columns 3 and 3. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #252.
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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: mint and sea green span only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
The tightest lines on puzzle #252
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 6 and 8 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, with 2 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 5 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.
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 #252 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 29. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
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.
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 #252 is column 1.
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 #252?
Puzzle #252 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #252 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #252, 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 #252?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.