8x8 Queens Puzzle #261

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 #261

What follows is a complete solve of puzzle #261, 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 shadow.

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

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

  1. Step 1. 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: 8 squares in all.

  2. Step 2. 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: 6 squares come off.

  3. Step 3. Only row 3, column 1 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 1, in blue and in the ring around that square is now dead.

  4. Step 4. The mint region is down to one open square, at row 4, column 5. Every colour holds exactly one queen, so that square is forced. Row 4 and column 5 are now spoken for, along with the squares touching that queen.

    Puzzle #261 after step 4: 2 of 8 queens placed
    The board after step 4 — 2 of 8 queens placed.

  5. Step 5. Red is down to 3 candidates in rows 6 and 7, columns 4 and 6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.

  6. Step 6. All of the pale yellow region's remaining squares (3 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 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: indigo has one square left, so its queen takes row 1, column 3; khaki has one square left, so its queen takes row 8, column 4; red has one square left, so its queen takes row 6, column 6; pale yellow has one square left, so its queen takes row 7, column 2; slate has one square left, so its queen takes row 5, column 8; amber has one square left, so its queen takes row 2, column 7. 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 7.

    Puzzle #261 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 #261

Puzzle #261 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.

As with every puzzle in this collection, #261 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.

How the colors divide this board

From smallest to largest, the regions on puzzle #261 are: indigo (2 squares), amber (2 squares), blue (4 squares), red (5 squares), pale yellow (10 squares), khaki (10 squares), mint (15 squares), slate (16 squares). An even split would hand every color 8 squares, so the indigo region is running 6 squares under that average while the slate region is the roomiest area on the grid with 16 squares.

Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So indigo, with 2 squares, is under far more pressure than slate with 16. A 14-square gap like this one rewards players who start where the choices are fewest.

Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #261, packing 100% of its 1×2 bounding box, whereas khaki straggles across its 5×4 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a hard board.

Indigo: 2 squares across rows 1–1, columns 2–3. It never leaves row 1, so its queen is locked to that row.

Amber covers 2 squares, spanning 1 row and 2 columns (rows 2–2, columns 7–8). It never leaves row 2, so its queen is locked to that row.

Blue occupies 4 squares within rows 1–3, columns 1–2.

Red: 5 squares across rows 5–7, columns 4–6.

Pale yellow covers 10 squares, spanning 5 rows and 3 columns (rows 4–8, columns 1–3).

Khaki occupies 10 squares within rows 4–8, columns 2–5.

Mint: 15 squares across rows 1–4, columns 2–8.

Slate covers 16 squares, spanning 6 rows and 3 columns (rows 3–8, columns 6–8).

Where to start on this board

Open on the tightest color. Here that is indigo, confined to 2 squares between rows 1 and 1 and columns 2 and 3. Its queen has nowhere else to go, which means those 1 row and 2 columns carry more constraint than anywhere else on #261.

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. 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 #261

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3 and 8 are the narrowest, touched by only 3 colors. Column 1 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 7 rows. Row 7 is the crowded extreme at 4 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.

The whole middle game reduces to two sweeps. Sweep the eight colors looking for one with a single square left; sweep the eight rows and eight columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 8x8 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 #261 is rated hard

The hard label comes out of four measurable things about #261: two of its regions are locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 3 colors, and its largest and smallest regions differ by 14. Boards that score tight on those measures give up their first queen fast.

Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.

A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.

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.

Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #261, start hunting for it near column 1.

A non-spoiling distribution check: solved, #261 carries 4 queens on the perimeter against 4 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 8x8 Queens puzzle #261?

Puzzle #261 is rated hard. 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 8x8 puzzle #261 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #261, 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 #261?

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