8x8 Queens Puzzle #95
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 13-step reasoning is written out below.
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Step-by-step solution for puzzle #95
What follows is a complete solve of puzzle #95, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 8 queen placements and 5 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: last square in a region, region confined to one line, region shadow, last square in a row.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Only row 1, column 8 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 8, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The amber region is down to one open square, at row 2, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 5, the remaining amber squares, and the ring of neighbours around row 2, column 5.
Step 3. Only row 7, column 4 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 4, in pale yellow and in the ring around that square is now dead.
The board after step 3 — 3 of 8 queens placed. Step 4. All of the mint region's remaining squares (2 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
Step 5. Blue is down to 3 candidates in rows 3–5, columns 3 and 6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 6. All of the red region's remaining squares (2 open squares) lie in column 6. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.
The board after step 6 — 3 of 8 queens placed. Step 7. Blue cannot leave column 3 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 2 squares in all.
Step 8. Slate is down to 4 candidates in rows 3–6, columns 1 and 2, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about slate itself.
Step 9. 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: row 5 is down to one square, putting a queen on row 5, column 2; blue has one square left, so its queen takes row 3, column 3; mint has one square left, so its queen takes row 4, column 7; khaki has one square left, so its queen takes row 8, column 1; red has one square left, so its queen takes row 6, column 6. 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 6, column 6.
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 #95
8x8 puzzle #95 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.
Like every board on this site, #95 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 #95 are: indigo (1 square), amber (3 squares), pale yellow (3 squares), khaki (7 squares), slate (8 squares), red (11 squares), mint (12 squares), blue (19 squares). An even split would hand every color 8 squares, so the indigo region is running 7 squares under that average while the blue region is the roomiest area on the grid with 19 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Indigo is working with 1 square while blue has 19 to spare, a gap of 18. Attack the cramped end and the roomy regions tend to resolve themselves.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #95, packing 100% of its 1×1 bounding box, whereas khaki straggles across its 4×4 box at just 44%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #95 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.
Indigo occupies 1 square within rows 1–1, columns 8–8. It never leaves row 1, so its queen is locked to that row.
Amber: 3 squares across rows 1–2, columns 5–6.
Pale yellow covers 3 squares, spanning 2 rows and 2 columns (rows 7–8, columns 4–5).
Khaki occupies 7 squares within rows 5–8, columns 1–4.
Slate: 8 squares across rows 3–7, columns 1–3.
Red covers 11 squares, spanning 4 rows and 4 columns (rows 5–8, columns 5–8).
Mint occupies 12 squares within rows 1–6, columns 5–8.
Blue: 19 squares across rows 1–7, columns 1–6.
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 1 square inside a 1×1 window running from row 1 to row 1 and column 8 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 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 and pale yellow 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 #95
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 3, 4 and 8 are the narrowest, touched by only 3 colors. Column 7 is the tightest column, with 2 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 7 rows. By contrast row 7 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 #95 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.
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 #95 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 18. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
If #95 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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around column 7 on this board.
As a sanity check rather than a spoiler: the finished solution to #95 puts 2 queens on the outer border and 6 queens in the interior, 2 of them in an actual 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
- 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 #95?
Puzzle #95 is rated medium. Its smallest color region holds 1 square, 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 #95 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #95, 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 #95?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.