8x8 Queens Puzzle #195
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 12-step reasoning is written out below.
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Step-by-step solution for puzzle #195
What follows is a complete solve of puzzle #195, 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: last square in a region, region confined to one line, region shadow, last square in a column.
Show the full walkthrough (9 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: indigo has one square left, so its queen takes row 1, column 6; blue has one square left, so its queen takes row 3, column 3; amber has one square left, so its queen takes row 2, column 1; slate has one square left, so its queen takes row 5, column 2. 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 5, column 2.
Step 2. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 1 square in all.
Step 3. The red region has 5 squares left, spread across rows 6 and 7, columns 4, 5, 7, and 8. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
The board after step 3 — 4 of 8 queens placed. Step 4. Khaki cannot leave row 8 — every one of its open squares (2 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 4 squares in all.
Step 5. Column 4 now has exactly one open square, row 8, column 4, in the khaki region. Columns must each hold a queen, so that placement is forced. Everything else in row 8, in column 4, in khaki and in the ring around that square is now dead.
Step 6. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 2 squares in all.
The board after step 6 — 5 of 8 queens placed. Step 7. The red region is down to one open square, at row 6, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 5, the remaining red squares, and the ring of neighbours around row 6, column 5.
Step 8. Only row 4, column 8 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 8, in mint and in the ring around that square is now dead.
Step 9. The pale yellow region is down to one open square, at row 7, column 7. Every colour holds exactly one queen, so that square is forced. Row 7 and column 7 are now spoken for, along with the squares touching that queen.
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 #195
8x8 puzzle #195 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, #195 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 #195 are: indigo (1 square), blue (1 square), pale yellow (5 squares), slate (6 squares), amber (11 squares), mint (12 squares), khaki (13 squares), red (15 squares). An even split would hand every color 8 squares, so the indigo region is running 7 squares under that average while the red region is the roomiest area on the grid with 15 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 1 place to put its queen; red has 15. The spread between them on this board is 14 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 indigo is the most solid, filling 100% of its 1×1 box, and red the most diffuse at 50% of its 5×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #195 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: 1 square across rows 1–1, columns 6–6. It never leaves row 1, so its queen is locked to that row.
Blue covers 1 square, spanning 1 row and 1 column (rows 3–3, columns 3–3). It never leaves row 3, so its queen is locked to that row.
Pale yellow occupies 5 squares within rows 7–8, columns 6–8.
Slate: 6 squares across rows 3–6, columns 1–2.
Amber covers 11 squares, spanning 3 rows and 5 columns (rows 1–3, columns 1–5).
Mint occupies 12 squares within rows 1–5, columns 5–8.
Khaki: 13 squares across rows 5–8, columns 1–6.
Red covers 15 squares, spanning 5 rows and 6 columns (rows 3–7, columns 3–8).
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 6 to column 6. 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. Blue 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 #195
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2 and 8 are the narrowest, touched by only 2 colors. Columns 1, 2, 4, 7 and 8 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
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.
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.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #195 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 14. 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 #195 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 #195 the place to look for one is around row 2.
As a sanity check rather than a spoiler: the finished solution to #195 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
- 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 #195?
Puzzle #195 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 8x8 puzzle #195 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #195, 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 #195?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.