11x11 Queens Puzzle #256

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 18-step reasoning is written out below.

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Step-by-step solution for puzzle #256

What follows is a complete solve of puzzle #256, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 11 queen placements and 7 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 confined to one line, region shadow, pairing argument on rows, pairing argument on columns.

Show the full walkthrough (11 steps) — contains the solution

  1. Step 1. Only row 5, column 1 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 1, the rest of the slate region and every square adjacent to it — diagonals included.

  2. Step 2. The pale yellow region is down to one open square, at row 7, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 4, the remaining pale yellow squares, and the ring of neighbours around row 7, column 4.

  3. Step 3. 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: 9 squares in all.

  4. Step 4. Wherever red ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

    Puzzle #256 after step 4: 2 of 11 queens placed
    The board after step 4 — 2 of 11 queens placed.

  5. Step 5. Amber, blue, and mint are now boxed into rows 2–4 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.

  6. Step 6. The red region is down to one open square, at row 6, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 7, the remaining red squares, and the ring of neighbours around row 6, column 7.

  7. Step 7. Wherever teal 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.

    Puzzle #256 after step 7: 3 of 11 queens placed
    The board after step 7 — 3 of 11 queens placed.

  8. Step 8. Here is the pairing argument. The indigo and mint regions have no open squares outside columns 2 and 3 — 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: 7 squares come off in one stroke.

  9. Step 9. The orange region has 3 squares left, spread across rows 9 and 11, columns 5 and 6. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.

  10. Step 10. Here is the pairing argument. The amber, khaki, and orange regions have no open squares outside columns 5, 6, and 8 — 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: 2 squares come off in one stroke.

  11. Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: teal has one square left, so its queen takes row 11, column 9; orange has one square left, so its queen takes row 9, column 5; khaki has one square left, so its queen takes row 8, column 8; amber has one square left, so its queen takes row 2, column 6; sea green has one square left, so its queen takes row 10, column 11; blue has one square left, so its queen takes row 3, column 10; mint has one square left, so its queen takes row 4, column 3; indigo has one square left, so its queen takes row 1, 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 1, column 2.

    Puzzle #256 after step 11: 11 of 11 queens placed
    The board after step 11 — 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 #256

This is puzzle number 256 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 #256 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 #256 are: slate (1 square), pale yellow (1 square), indigo (5 squares), teal (5 squares), blue (11 squares), red (12 squares), mint (13 squares), sea green (13 squares), amber (16 squares), khaki (21 squares), orange (23 squares). An even split would hand every color 11 squares, so the slate region is running 10 squares under that average while the orange region is the roomiest area on the grid with 23 squares.

Every color takes one queen and one only, whatever its size — which is why the 22 square difference between slate and orange 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 slate is the most solid, filling 100% of its 1×1 box, and khaki the most diffuse at 43% of its 7×7 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 #256, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Slate covers 1 square, spanning 1 row and 1 column (rows 5–5, columns 1–1). It never leaves row 5, so its queen is locked to that row.

Pale yellow occupies 1 square within rows 7–7, columns 4–4. It never leaves row 7, so its queen is locked to that row.

Indigo: 5 squares across rows 1–2, columns 1–4.

Teal covers 5 squares, spanning 2 rows and 3 columns (rows 10–11, columns 7–9).

Blue occupies 11 squares within rows 1–5, columns 9–11.

Red: 12 squares across rows 3–7, columns 4–8.

Mint covers 13 squares, spanning 5 rows and 4 columns (rows 2–6, columns 1–4).

Sea green occupies 13 squares within rows 6–11, columns 9–11.

Amber: 16 squares across rows 1–4, columns 4–9.

Khaki covers 21 squares, spanning 7 rows and 7 columns (rows 4–10, columns 4–10).

Orange occupies 23 squares within rows 6–11, columns 1–6.

Where to start on this board

Open on the tightest color. Here that is slate, confined to 1 square between rows 5 and 5 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 #256.

Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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. Pale yellow, indigo and teal 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 #256

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 8, 9 and 11 are the narrowest, touched by only 3 colors. Column 11 is the tightest column, with 2 colors.

A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 7 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.

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 #256 is rated hard

The rating reflects how much the board concedes up front. Puzzle #256 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 22 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

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 hard 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.

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 #256 is column 11.

A non-spoiling distribution check: solved, #256 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

  1. The board is an N×N grid divided into N colored regions.
  2. Place exactly one queen (♛) in each row, each column, and each colored region.
  3. No two queens may touch each other — not horizontally, vertically, or diagonally.
  4. 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.
  5. 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 #256?

Puzzle #256 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.

Does 11x11 puzzle #256 have only one solution?

Yes. Every puzzle in the 11x11 collection, including #256, 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 #256?

Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.