11x11 Queens Puzzle #53

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 17-step reasoning is written out below.

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Step-by-step solution for puzzle #53

What follows is a complete solve of puzzle #53, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 11 queen placements and 6 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: region shadow, region confined to one line, pairing argument on rows, last square in a region, last square in a row.

Show the full walkthrough (8 steps) — contains the solution

  1. Step 1. Wherever amber 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.

  2. Step 2. All of the khaki region's remaining squares (4 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.

  3. Step 3. Sea green cannot leave row 10 — every one of its open squares (2 open squares) sits there. That row belongs to sea green, so every square on it owned by another colour is dead: 13 squares in all.

  4. Step 4. Here is the pairing argument. The khaki, orange, and teal regions have no open squares outside rows 8, 9, and 11 — 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: 15 squares come off in one stroke.

    Puzzle #53 after step 4: 0 of 11 queens placed
    The board after step 4 — 0 of 11 queens placed.

  5. 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 9; slate has one square left, so its queen takes row 5, column 10; 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 5; sea green has one square left, so its queen takes row 10, column 3; row 8 is down to one square, putting a queen on row 8, column 1. 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 1.

  6. Step 6. Indigo is down to 6 candidates in rows 1–4, columns 7 and 8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.

  7. Step 7. All of the amber region's remaining squares (2 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.

  8. Step 8. 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: mint has one square left, so its queen takes row 4, column 8; indigo has one square left, so its queen takes row 1, column 7; amber has one square left, so its queen takes row 2, column 11; teal has one square left, so its queen takes row 11, column 6; blue has one square left, so its queen takes row 3, 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 3, column 4.

    Puzzle #53 after step 8: 11 of 11 queens placed
    The board after step 8 — 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 #53

Puzzle #53 is one of the easy-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.

Puzzle #53 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 #53 are: sea green (2 squares), amber (4 squares), khaki (4 squares), slate (6 squares), mint (10 squares), orange (10 squares), teal (10 squares), indigo (14 squares), red (16 squares), pale yellow (16 squares), blue (29 squares). An even split would hand every color 11 squares, so the sea green region is running 9 squares under that average while the blue region is the roomiest area on the grid with 29 squares.

Every color takes one queen and one only, whatever its size — which is why the 27 square difference between sea green and blue 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 4×1 box that encloses it, while red is the most scattered at 33% of its 7×7 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 #53, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Sea green occupies 2 squares within rows 10–10, columns 3–4. It never leaves row 10, so its queen is locked to that row.

Amber: 4 squares across rows 1–2, columns 9–11.

Khaki covers 4 squares, spanning 4 rows and 1 column (rows 8–11, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.

Slate occupies 6 squares within rows 5–8, columns 10–11.

Mint: 10 squares across rows 3–6, columns 8–11.

Orange covers 10 squares, spanning 4 rows and 4 columns (rows 8–11, columns 2–5).

Teal occupies 10 squares within rows 9–11, columns 5–8.

Indigo: 14 squares across rows 1–7, columns 7–10.

Red covers 16 squares, spanning 7 rows and 7 columns (rows 2–8, columns 1–7).

Pale yellow occupies 16 squares within rows 7–11, columns 4–11.

Blue: 29 squares across rows 1–6, columns 1–7.

Where to start on this board

Sea green is the natural opening on #53: it is the smallest region on the grid at 2 squares, boxed into rows 10–10 and columns 3–4. Since one of those squares must hold a queen, that block of 1 row and 2 columns is the most contested part of the board.

Because sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. 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 is no more than two rows tall, so its queen is 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 #53

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

Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 10 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.

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.

The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.

Why puzzle #53 is rated easy

The rating reflects how much the board concedes up front. Puzzle #53 has two regions confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 27 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.

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 #53 is row 1.

As a sanity check rather than a spoiler: the finished solution to #53 puts 4 queens on the outer border and 7 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.

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 #53?

Puzzle #53 is rated easy. Its smallest color region holds 2 squares, 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 #53 have only one solution?

Yes. Every puzzle in the 11x11 collection, including #53, 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 #53?

Start with the sea green region — the most constrained color on this board, with 2 squares spanning rows 10–10 and columns 3–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.