11x11 Queens Puzzle #296

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 14-step reasoning is written out below.

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Step-by-step solution for puzzle #296

What follows is a complete solve of puzzle #296, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 11 queen placements and 3 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 region confined to one line.

Techniques this board needs: last square in a region, region confined to one line.

Show the full walkthrough (7 steps) — contains the solution

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

  2. Step 2. The teal region is down to one open square, at row 11, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 11, the remaining teal squares, and the ring of neighbours around row 11, column 11.

  3. Step 3. Amber cannot leave row 2 — every one of its open squares (3 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 5 squares in all.

  4. Step 4. All of the blue region's remaining squares (3 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.

    Puzzle #296 after step 4: 2 of 11 queens placed
    The board after step 4 — 2 of 11 queens placed.

  5. Step 5. 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: mint has one square left, so its queen takes row 4, column 2; red has one square left, so its queen takes row 6, column 1; khaki has one square left, so its queen takes row 8, column 3; slate has one square left, so its queen takes row 5, 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 5, column 4.

  6. Step 6. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 3 squares in all.

  7. Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: orange has one square left, so its queen takes row 9, column 6; pale yellow has one square left, so its queen takes row 7, column 8; blue has one square left, so its queen takes row 3, column 7; sea green has one square left, so its queen takes row 10, column 9; amber has one square left, so its queen takes row 2, column 10. 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 2, column 10.

    Puzzle #296 after step 7: 11 of 11 queens placed
    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 #296

This is puzzle number 296 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 #296 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 #296 are: indigo (1 square), teal (1 square), red (6 squares), amber (7 squares), blue (10 squares), khaki (10 squares), slate (11 squares), mint (14 squares), orange (18 squares), sea green (18 squares), pale yellow (25 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the pale yellow region is the roomiest area on the grid with 25 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Indigo is working with 1 square while pale yellow has 25 to spare, a gap of 24. Attack the cramped end and the roomy regions tend to resolve themselves.

Shape matters as much as size. The indigo 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 52% of its 8×6 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

Here is the full footprint of every color on puzzle #296, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Indigo occupies 1 square within rows 1–1, columns 5–5. It never leaves row 1, so its queen is locked to that row.

Teal: 1 square across rows 11–11, columns 11–11. It never leaves row 11, so its queen is locked to that row.

Red covers 6 squares, spanning 3 rows and 3 columns (rows 4–6, columns 1–3).

Amber occupies 7 squares within rows 1–2, columns 8–11.

Blue: 10 squares across rows 1–3, columns 5–9.

Khaki covers 10 squares, spanning 5 rows and 3 columns (rows 7–11, columns 1–3).

Slate occupies 11 squares within rows 4–7, columns 2–6.

Mint: 14 squares across rows 1–4, columns 1–5.

Orange covers 18 squares, spanning 5 rows and 5 columns (rows 7–11, columns 3–7).

Sea green occupies 18 squares within rows 6–11, columns 6–10.

Pale yellow: 25 squares across rows 3–10, columns 6–11.

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 5 and 5. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #296.

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. Teal and amber 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 #296

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 3 and 5 are the narrowest, touched by only 3 colors. Columns 1, 4, 10 and 11 are the tightest columns, with 3 colors.

The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 7, meeting 5 colors, is the opposite case — the busiest line on #296 and the last one you should expect to crack.

Working through the middle game

The middle of #296 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.

With eleven queens to seat and eleven regions competing over 121 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 11x11 boards quickly and players who stall halfway.

Resist the plausible-looking queen. On #296 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 #296 is rated hard

The rating reflects how much the board concedes up front. Puzzle #296 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 24 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.

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 2 on this board.

Here is a shape check that gives nothing away: when #296 is solved, 3 queens sit on the outer edge of the grid and 8 sit inside it, with 1 queen 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

  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 #296?

Puzzle #296 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 #296 have only one solution?

Yes. Every puzzle in the 11x11 collection, including #296, 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 #296?

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