8x8 Queens Puzzle #255
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #255
What follows is a complete solve of puzzle #255, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 8 queen placements and 11 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 line confined to one region.
Techniques this board needs: region confined to one line, last square in a region, region shadow, line confined to one region, last square in a column, last square in a row.
Show the full walkthrough (16 steps) — contains the solution
Step 1. Mint cannot leave column 1 — every one of its open squares (3 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 6 squares in all.
Step 2. The amber region is down to one open square, at row 2, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 2, the remaining amber squares, and the ring of neighbours around row 2, column 2.
Step 3. Pale yellow cannot leave column 8 — every one of its open squares (4 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 3 squares in all.
Step 4. Wherever slate ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 5. Red is down to 6 candidates in rows 5–8, columns 5–7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
The board after step 5 — 1 of 8 queens placed. Step 6. The khaki region has 4 squares left, spread across rows 6–8, columns 3 and 4. 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.
Step 7. Row 1 has only indigo squares left (4 open squares). The row needs a queen and only indigo can provide one, which pins that colour to this row and kills its squares elsewhere: 2 squares.
Step 8. Every open square left in row 3 (2 open squares) belongs to the blue region. Since that row must contain a queen, blue is the colour that supplies it — so blue squares anywhere else on the board are out, 7 squares in all.
Step 9. Scan column 3 and only row 8, column 3 remains — a khaki square. Every column takes a queen, so it takes this one. Row 8 and column 3 are now spoken for, along with the squares touching that queen.
Step 10. Column 4 now has exactly one open square, row 1, column 4, in the indigo region. Columns must each hold a queen, so that placement is forced. That clears row 1, column 4, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 11. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 1 square in all.
The board after step 11 — 3 of 8 queens placed. Step 12. Row 4 has a single open square left, at column 1 in the mint region. Every row needs a queen, so this one is forced. Cross out the whole of row 4 and column 1, the remaining mint squares, and the ring of neighbours around row 4, column 1.
Step 13. Wherever slate ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 14. Red is down to 4 candidates in rows 5–7, columns 5 and 6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
Step 15. Slate cannot leave column 7 — every one of its open squares (2 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 2 squares in all.
Step 16. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 6; pale yellow has one square left, so its queen takes row 7, column 8; slate has one square left, so its queen takes row 5, column 7; red has one square left, so its queen takes row 6, column 5. 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 5.
The board after step 16 — 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 #255
8x8 puzzle #255 is rated hard. 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 #255, 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 #255 are: mint (3 squares), amber (4 squares), pale yellow (4 squares), red (8 squares), slate (9 squares), indigo (10 squares), khaki (10 squares), blue (16 squares). An even split would hand every color 8 squares, so the mint region is running 5 squares under that average while the blue region is the roomiest area on the grid with 16 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Mint is working with 3 squares while blue has 16 to spare, a gap of 13. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here mint is the most solid, filling 100% of its 3×1 box, and blue the most diffuse at 44% of its 6×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
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.
Mint: 3 squares across rows 4–6, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Amber covers 4 squares, spanning 3 rows and 2 columns (rows 1–3, columns 1–2).
Pale yellow occupies 4 squares within rows 5–8, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.
Red: 8 squares across rows 5–8, columns 5–7.
Slate covers 9 squares, spanning 6 rows and 3 columns (rows 1–6, columns 6–8).
Indigo occupies 10 squares within rows 1–3, columns 2–7.
Khaki: 10 squares across rows 6–8, columns 1–5.
Blue covers 16 squares, spanning 6 rows and 6 columns (rows 2–7, columns 2–7).
Where to start on this board
Begin where the choices are fewest. On this board that means mint, which owns just 3 squares inside a 3×1 window running from row 4 to row 6 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because mint stays inside column 1, its queen belongs to that column and no other region may use it. Cross out the rest of column 1 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: amber spans only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
The tightest lines on puzzle #255
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 4 and 8 are the narrowest, touched by only 3 colors. Column 8 is the tightest column, with 2 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 6, meeting 6 colors, is the opposite case — the busiest line on #255 and the last one you should expect to crack.
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.
Resist the plausible-looking queen. On #255 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 #255 is rated hard
The hard label comes out of four measurable things about #255: two of its regions are locked to one row or column, its smallest color spans 3 squares, its least crowded row meets 3 colors, and its largest and smallest regions differ by 13. Boards that score tight on those measures give up their first queen fast.
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 #255 despite the hard 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.
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 8 on this board.
Here is a shape check that gives nothing away: when #255 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 #255?
Puzzle #255 is rated hard. Its smallest color region holds 3 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 #255 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #255, 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 #255?
Start with the mint region — the most constrained color on this board, with 3 squares spanning rows 4–6 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.