8x8 Queens Puzzle #281

Difficulty: hard. Place 8 queens on this 8x8 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 12-step reasoning is written out below.

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Step-by-step solution for puzzle #281

What follows is a complete solve of puzzle #281, worked the way a person works it rather than the way a computer does. It runs to 12 deductions — 8 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 region confined to one line.

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

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

  1. Step 1. Indigo cannot leave row 1 — every one of its open squares (4 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 4 squares in all.

  2. Step 2. All of the amber region's remaining squares (2 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. Only row 4, column 2 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 2, in mint and in the ring around that square is now dead.

  4. Step 4. The amber region is down to one open square, at row 2, column 1. Every colour holds exactly one queen, so that square is forced. Row 2 and column 1 are now spoken for, along with the squares touching that queen.

    Puzzle #281 after step 4: 2 of 8 queens placed
    The board after step 4 — 2 of 8 queens placed.

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

  6. Step 6. All of the slate region's remaining squares (2 open squares) lie in row 5. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.

  7. Step 7. 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: red has one square left, so its queen takes row 6, column 8; blue has one square left, so its queen takes row 3, column 6; khaki has one square left, so its queen takes row 8, column 7; indigo has one square left, so its queen takes row 1, column 5; slate has one square left, so its queen takes row 5, column 4; pale yellow has one square left, so its queen takes row 7, column 3. 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 7, column 3.

    Puzzle #281 after step 7: 8 of 8 queens placed
    The board after step 7 — 8 of 8 queens placed.

That completes the board: 8 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 8x8 Queens puzzle #281

Puzzle #281 is one of the hard-rated boards in the 8x8 set. Eight colors divide its 64 squares, and you win by placing eight queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.

Puzzle #281 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 #281 are: amber (2 squares), indigo (4 squares), mint (6 squares), red (7 squares), khaki (8 squares), blue (11 squares), slate (13 squares), pale yellow (13 squares). An even split would hand every color 8 squares, so the amber region is running 6 squares under that average while the pale yellow region is the roomiest area on the grid with 13 squares.

Every color takes one queen and one only, whatever its size — which is why the 11 square difference between amber 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.

Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #281, packing 100% of its 1×4 bounding box, whereas blue straggles across its 4×6 box at just 46%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Here is the full footprint of every color on puzzle #281, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Amber occupies 2 squares within rows 2–3, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.

Indigo: 4 squares across rows 1–1, columns 5–8. It never leaves row 1, so its queen is locked to that row.

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

Red occupies 7 squares within rows 3–6, columns 6–8.

Khaki: 8 squares across rows 6–8, columns 6–8.

Blue covers 11 squares, spanning 4 rows and 6 columns (rows 1–4, columns 3–8).

Slate occupies 13 squares within rows 3–6, columns 1–5.

Pale yellow: 13 squares across rows 6–8, columns 1–5.

Where to start on this board

Open on the tightest color. Here that is amber, confined to 2 squares between rows 2 and 3 and columns 1 and 1. Its queen has nowhere else to go, which means those 2 rows and 1 column carry more constraint than anywhere else on #281.

Because amber stays inside column 1, its queen belongs to that column and no other region may use it. Cross out the rest of column 1 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.

Work outward to the other flat regions next. Indigo 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 #281

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5, 7 and 8 are the narrowest, touched by only 2 colors. Columns 2, 3 and 4 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 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 7 rows. By contrast row 3 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

The middle of #281 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.

Keep alternating between two views of the board. In the region view you ask which of the eight colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 8x8 board unwinds.

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 #281 is rated hard

The rating reflects how much the board concedes up front. Puzzle #281 has two regions confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 11 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 8x8

At 8x8 the whole grid stays within a single glance, which makes systematic scanning practical. Read the rows in order and count the colors in each — a row touched by two colors is far more constrained than one touched by five, and that is usually where the next forced move hides. The board is small enough that re-scanning from the top after each placement costs almost nothing.

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 #281 is row 5.

As a sanity check rather than a spoiler: the finished solution to #281 puts 4 queens on the outer border and 4 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 8x8 Queens puzzle #281?

Puzzle #281 is rated hard. Its smallest color region holds 2 squares, 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 8x8 puzzle #281 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #281, has been verified to have exactly one valid arrangement of eight queens, and it can always be reached by logic alone — no guessing or backtracking needed.

Where should I place my first queen on puzzle #281?

Start with the amber region — the most constrained color on this board, with 2 squares spanning rows 2–3 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.