8x8 Queens Puzzle #6
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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #6
What follows is a complete solve of puzzle #6, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 8 queen placements and 7 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, line confined to one region, last square in a column.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Wherever amber ends up among its 3 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
Step 2. All of the khaki region's remaining squares (2 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.
Step 3. Pale yellow cannot leave column 1 — every one of its open squares (3 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 5 squares in all.
The board after step 3 — 0 of 8 queens placed. Step 4. Wherever indigo ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 5. Indigo and amber are now boxed into rows 1 and 2 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 5 squares at once.
Step 6. The blue region is down to one open square, at row 3, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 8, the remaining blue squares, and the ring of neighbours around row 3, column 8.
The board after step 6 — 1 of 8 queens placed. Step 7. Mint cannot leave row 4 — every one of its open squares (3 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 2 squares in all.
Step 8. Every open square left in column 4 (3 open squares) belongs to the red region. Since that column must contain a queen, red is the colour that supplies it — so red squares anywhere else on the board are out, 8 squares in all.
Step 9. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: column 7 is down to one square, putting a queen on row 5, column 7; column 6 is down to one square, putting a queen on row 2, column 6; indigo has one square left, so its queen takes row 1, column 2; khaki has one square left, so its queen takes row 8, column 3; mint has one square left, so its queen takes row 4, column 5; red has one square left, so its queen takes row 6, column 4; pale yellow has one square left, so its queen takes row 7, 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 7, column 1.
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 #6
Board #6 of the 8x8 bank carries a hard rating. Its 64 squares are shared between eight colored regions, and the solution places eight queens: one per row, one per column, one per region, none of them side by side or corner to corner.
Like every board on this site, #6 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #6 are: khaki (2 squares), amber (3 squares), indigo (5 squares), pale yellow (5 squares), blue (6 squares), slate (9 squares), mint (15 squares), red (19 squares). An even split would hand every color 8 squares, so the khaki region is running 6 squares under that average while the red region is the roomiest area on the grid with 19 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 2 places to put its queen; red has 19. The spread between them on this board is 17 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Khaki is the densest region on this grid at 100% of a 1×2 frame; mint is the loosest, occupying only 54% of its 4×7 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Khaki: 2 squares across rows 8–8, columns 2–3. It never leaves row 8, so its queen is locked to that row.
Amber covers 3 squares, spanning 2 rows and 2 columns (rows 1–2, columns 5–6).
Indigo occupies 5 squares within rows 1–2, columns 1–3.
Pale yellow: 5 squares across rows 5–8, columns 1–2.
Blue covers 6 squares, spanning 3 rows and 3 columns (rows 1–3, columns 6–8).
Slate occupies 9 squares within rows 4–7, columns 5–8.
Mint: 15 squares across rows 1–4, columns 1–7.
Red covers 19 squares, spanning 5 rows and 7 columns (rows 4–8, columns 2–8).
Where to start on this board
Khaki is the natural opening on #6: it is the smallest region on the grid at 2 squares, boxed into rows 8–8 and columns 2–3. 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 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. Indigo 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 #6
A quick way to find the next move is to count how many different colors touch each line. On this board, row 3 is the narrowest, touched by only 2 colors. Column 4 is the tightest column, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 7 rows. Row 2, meeting 4 colors, is the opposite case — the busiest line on #6 and the last one you should expect to crack.
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.
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.
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 #6 is rated hard
Ratings track how generous the opening is. On #6 you get one region pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 17-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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.
If #6 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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 #6 the place to look for one is around row 3.
Here is a shape check that gives nothing away: when #6 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
- The board is an N×N grid divided into N colored regions.
- Place exactly one queen (♛) in each row, each column, and each colored region.
- No two queens may touch each other — not horizontally, vertically, or diagonally.
- 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.
- 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 #6?
Puzzle #6 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 8x8 puzzle #6 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #6, 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 #6?
Start with the khaki region — the most constrained color on this board, with 2 squares spanning rows 8–8 and columns 2–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.