8x8 Queens Puzzle #271

About 8x8 Queens puzzle #271

8x8 puzzle #271 is rated easy. 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, #271 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 #271 are: mint (1 square), slate (1 square), red (1 square), indigo (5 squares), blue (6 squares), pale yellow (12 squares), khaki (14 squares), amber (24 squares). An even split would hand every color 8 squares, so the mint region is running 7 squares under that average while the amber region is the roomiest area on the grid with 24 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Mint is working with 1 square while amber has 24 to spare, a gap of 23. 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 1×1 box, and blue the most diffuse at 50% of its 3×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

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.

Mint covers 1 square, spanning 1 row and 1 column (rows 4–4, columns 7–7). It never leaves row 4, so its queen is locked to that row.

Slate occupies 1 square within rows 5–5, columns 2–2. It never leaves row 5, so its queen is locked to that row.

Red: 1 square across rows 6–6, columns 8–8. It never leaves row 6, so its queen is locked to that row.

Indigo covers 5 squares, spanning 2 rows and 4 columns (rows 1–2, columns 1–4).

Blue occupies 6 squares within rows 3–5, columns 1–4.

Pale yellow: 12 squares across rows 5–8, columns 1–5.

Khaki covers 14 squares, spanning 4 rows and 6 columns (rows 5–8, columns 3–8).

Amber occupies 24 squares within rows 1–5, columns 1–8.

Where to start on this board

Begin where the choices are fewest. On this board that means mint, which owns just 1 square inside a 1×1 window running from row 4 to row 4 and column 7 to column 7. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Because mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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. Slate, red and indigo 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 #271

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 7 and 8 are the narrowest, touched by only 2 colors. Column 6 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 5, meeting 5 colors, is the opposite case — the busiest line on #271 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.

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 #271 is rated easy

Ratings track how generous the opening is. On #271 you get six regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 23-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.

The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a easy board from the rest.

If #271 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 row 1 on this board.

Here is a shape check that gives nothing away: when #271 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.