11x11 Queens Puzzle #257
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 #257
What follows is a complete solve of puzzle #257, 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: last square in a region, region shadow, pairing argument on rows, pairing argument on columns, region confined to one line.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Only row 8, column 1 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 1, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 2. Amber is down to 3 candidates in rows 1 and 2, columns 4 and 5, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The orange region has 4 squares left, spread across rows 6, 7, and 9, columns 10 and 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.
Step 4. Here is the pairing argument. The indigo and amber regions have no open squares outside rows 1 and 2 — 2 colours confined to 2 rows. Between them they must take one row 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 4 — 1 of 11 queens placed. Step 5. Blue is down to 4 candidates in rows 3 and 4, columns 6, 8, and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 6. Here is the pairing argument. The blue, mint, and slate regions have no open squares outside rows 3–5 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 13 squares come off in one stroke.
Step 7. Red, pale yellow, and orange are now boxed into rows 6, 7, and 9 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 4 squares at once.
Step 8. Here is the pairing argument. The slate and orange regions have no open squares outside columns 10 and 11 — 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: 8 squares come off in one stroke.
The board after step 8 — 1 of 11 queens placed. Step 9. 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: 1 square in all.
Step 10. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 11. Teal cannot leave column 9 — every one of its open squares (2 open squares) sits there. That column belongs to teal, so every square in it owned by another colour is dead: 7 squares in all.
Step 12. 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: indigo has one square left, so its queen takes row 1, column 8; blue has one square left, so its queen takes row 3, column 6; amber has one square left, so its queen takes row 2, column 4; mint has one square left, so its queen takes row 4, column 3; slate has one square left, so its queen takes row 5, column 11; red has one square left, so its queen takes row 6, column 2; orange has one square left, so its queen takes row 9, column 10; pale yellow has one square left, so its queen takes row 7, column 7; teal has one square left, so its queen takes row 11, column 9; sea green has one square left, so its queen takes row 10, column 5. 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 10, column 5.
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 #257
Puzzle #257 is one of the medium-rated boards in the 11x11 set. Eleven colors divide its 121 squares, and you win by placing eleven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
There is exactly one way to finish #257, 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 #257 are: khaki (1 square), amber (3 squares), indigo (5 squares), orange (5 squares), slate (6 squares), teal (7 squares), blue (10 squares), mint (16 squares), red (16 squares), sea green (22 squares), pale yellow (30 squares). An even split would hand every color 11 squares, so the khaki region is running 10 squares under that average while the pale yellow 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 khaki and pale yellow 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.
Shape matters as much as size. The khaki region is the most compact color here, filling 100% of the 1×1 box that encloses it, while pale yellow is the most scattered at 54% of its 7×8 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
Region by region
Below is every color on #257 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.
Khaki occupies 1 square within rows 8–8, columns 1–1. It never leaves row 8, so its queen is locked to that row.
Amber: 3 squares across rows 1–2, columns 4–5.
Indigo covers 5 squares, spanning 2 rows and 4 columns (rows 1–2, columns 8–11).
Orange occupies 5 squares within rows 6–9, columns 10–11.
Slate: 6 squares across rows 2–5, columns 10–11.
Teal covers 7 squares, spanning 3 rows and 3 columns (rows 9–11, columns 9–11).
Blue occupies 10 squares within rows 1–4, columns 6–9.
Mint: 16 squares across rows 1–5, columns 1–5.
Red covers 16 squares, spanning 6 rows and 4 columns (rows 4–9, columns 1–4).
Sea green occupies 22 squares within rows 7–11, columns 1–8.
Pale yellow: 30 squares across rows 3–9, columns 3–10.
Where to start on this board
Khaki is the natural opening on #257: it is the smallest region on the grid at 1 square, boxed into rows 8–8 and columns 1–1. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because khaki never leaves row 8, its queen must be in that row — and that instantly settles row 8 for everyone else. Sweep along it and X out every square that is not khaki. 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. Amber 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 #257
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 10 and 11 are the narrowest, touched by only 2 colors. Columns 2, 6 and 7 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 9, meeting 5 colors, is the opposite case — the busiest line on #257 and the last one you should expect to crack.
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.
The whole middle game reduces to two sweeps. Sweep the eleven colors looking for one with a single square left; sweep the eleven rows and eleven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 11x11 solve from a stalled one.
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 #257 is rated medium
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 2 colors, and a region-size spread of 29. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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 medium board from the rest.
Stuck on #257 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 #257 is row 10.
Here is a shape check that gives nothing away: when #257 is solved, 4 queens sit on the outer edge of the grid and 7 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #257?
Puzzle #257 is rated medium. Its smallest color region holds 1 square, 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 #257 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #257, 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 #257?
Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.