8x8 Queens Puzzle #67

Difficulty: medium. 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 14-step reasoning is written out below.

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Step-by-step solution for puzzle #67

What follows is a complete solve of puzzle #67, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 8 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 columns.

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

Show the full walkthrough (9 steps) — contains the solution

  1. Step 1. Khaki cannot leave row 8 — every one of its open squares (3 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 6 squares in all.

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

  3. Step 3. Only row 6, column 6 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 6, in red and in the ring around that square is now dead.

    Puzzle #67 after step 3: 2 of 8 queens placed
    The board after step 3 — 2 of 8 queens placed.

  4. Step 4. Wherever amber ends up among its 3 squares, the same squares fall within reach of it — 4 squares in total, impossible regardless of how the colour resolves.

  5. Step 5. Slate is down to 4 candidates in rows 3–5, columns 3–5, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about slate itself.

  6. Step 6. All of the mint 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: 3 squares come off.

    Puzzle #67 after step 6: 2 of 8 queens placed
    The board after step 6 — 2 of 8 queens placed.

  7. Step 7. Wherever indigo 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.

  8. Step 8. Here is the pairing argument. The blue and khaki regions have no open squares outside columns 7 and 8 — 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: 1 square come off in one stroke.

  9. Step 9. 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: amber has one square left, so its queen takes row 2, column 5; indigo has one square left, so its queen takes row 1, column 3; slate has one square left, so its queen takes row 5, column 4; mint has one square left, so its queen takes row 4, column 1; blue has one square left, so its queen takes row 3, column 8; khaki has one square left, so its queen takes row 8, 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 8, column 7.

    Puzzle #67 after step 9: 8 of 8 queens placed
    The board after step 9 — 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 #67

8x8 puzzle #67 is rated medium. Eight colored regions cover its 64 squares, and your job is to seat eight queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.

There is exactly one way to finish #67, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these eight regions is what sets the depth.

How the colors divide this board

From smallest to largest, the regions on puzzle #67 are: khaki (3 squares), pale yellow (5 squares), amber (7 squares), indigo (8 squares), red (8 squares), slate (10 squares), mint (11 squares), blue (12 squares). An even split would hand every color 8 squares, so the khaki region is running 5 squares under that average while the blue region is the roomiest area on the grid with 12 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Khaki has only 3 places to put its queen; blue has 12. The spread between them on this board is 9 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

A region's outline can constrain it more than its size does. Here khaki is the most solid, filling 100% of its 1×3 box, and amber the most diffuse at 44% of its 4×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

Below is every color on #67 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.

Khaki covers 3 squares, spanning 1 row and 3 columns (rows 8–8, columns 6–8). It never leaves row 8, so its queen is locked to that row.

Pale yellow occupies 5 squares within rows 7–8, columns 1–4.

Amber: 7 squares across rows 1–4, columns 4–7.

Indigo covers 8 squares, spanning 3 rows and 5 columns (rows 1–3, columns 1–5).

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

Slate: 10 squares across rows 3–6, columns 3–5.

Mint covers 11 squares, spanning 6 rows and 4 columns (rows 2–7, columns 1–4).

Blue occupies 12 squares within rows 1–6, columns 6–8.

Where to start on this board

Begin where the choices are fewest. On this board that means khaki, which owns just 3 squares inside a 1×3 window running from row 8 to row 8 and column 6 to column 8. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Because khaki never leaves row 8, its queen must be in that row — and that instantly settles row 8 for everyone else. Sweep along it and X out every square that is not khaki. 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 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 #67

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 5, 7 and 8 are the narrowest, touched by only 3 colors. Columns 1, 2 and 8 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 7 rows. Row 3, meeting 5 colors, is the opposite case — the busiest line on #67 and the last one you should expect to crack.

Working through the middle game

The middle of #67 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 eight queens to seat and eight regions competing over 64 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 8x8 boards quickly and players who stall halfway.

Resist the plausible-looking queen. On #67 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 #67 is rated medium

What earns a board its rating is the shape of its opening. Here that opening offers one single-line region, a 3-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 9. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

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.

Stuck on #67 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.

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.

One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #67 the place to look for one is around row 1.

Here is a shape check that gives nothing away: when #67 is solved, 4 queens sit on the outer edge of the grid and 4 sit inside it, and no queen lands 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 8x8 Queens puzzle #67?

Puzzle #67 is rated medium. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.

Does 8x8 puzzle #67 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #67, 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 #67?

Start with the khaki region — the most constrained color on this board, with 3 squares spanning rows 8–8 and columns 6–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.