8x8 Queens Puzzle #171

About 8x8 Queens puzzle #171

8x8 puzzle #171 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.

As with every puzzle in this collection, #171 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.

How the colors divide this board

From smallest to largest, the regions on puzzle #171 are: red (1 square), blue (3 squares), amber (4 squares), pale yellow (4 squares), indigo (5 squares), slate (9 squares), khaki (18 squares), mint (20 squares). An even split would hand every color 8 squares, so the red region is running 7 squares under that average while the mint region is the roomiest area on the grid with 20 squares.

Every color takes one queen and one only, whatever its size — which is why the 19 square difference between red and mint is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.

A region's outline can constrain it more than its size does. Here amber is the most solid, filling 100% of its 2×2 box, and khaki the most diffuse at 56% of its 8×4 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.

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

Blue covers 3 squares, spanning 3 rows and 1 column (rows 1–3, columns 3–3). It sits wholly inside column 3, so its queen must be in that column.

Amber occupies 4 squares within rows 1–2, columns 7–8.

Pale yellow: 4 squares across rows 7–8, columns 3–5.

Indigo covers 5 squares, spanning 2 rows and 3 columns (rows 1–2, columns 4–6).

Slate occupies 9 squares within rows 3–6, columns 3–5.

Khaki: 18 squares across rows 1–8, columns 1–4.

Mint covers 20 squares, spanning 7 rows and 4 columns (rows 2–8, columns 5–8).

Where to start on this board

Begin where the choices are fewest. On this board that means red, which owns just 1 square inside a 1×1 window running from row 6 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 red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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, 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 #171

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 4, 5, 7 and 8 are the narrowest, touched by only 3 colors. Column 2 is the tightest column, with 1 color.

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 2, meeting 5 colors, is the opposite case — the busiest line on #171 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.

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.

Resist the plausible-looking queen. On #171 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 #171 is rated hard

Ratings track how generous the opening is. On #171 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 19-square gap between the largest and smallest regions. Those four numbers largely explain the hard 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 hard board from the rest.

A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.

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.

There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #171 is column 2.

Here is a shape check that gives nothing away: when #171 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.