8x8 Queens Puzzle #129

About 8x8 Queens puzzle #129

Puzzle #129 is one of the medium-rated boards in the 8x8 set. Eight colors divide its 64 squares, and you win by placing eight queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.

As with every puzzle in this collection, #129 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 #129 are: indigo (2 squares), red (3 squares), amber (4 squares), slate (5 squares), pale yellow (7 squares), khaki (12 squares), blue (14 squares), mint (17 squares). An even split would hand every color 8 squares, so the indigo region is running 6 squares under that average while the mint region is the roomiest area on the grid with 17 squares.

Every color takes one queen and one only, whatever its size — which is why the 15 square difference between indigo 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.

Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #129, packing 100% of its 2×1 bounding box, whereas slate straggles across its 3×3 box at just 56%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Below is every color on #129 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: 2 squares across rows 1–2, columns 2–2. It sits wholly inside column 2, so its queen must be in that column.

Red covers 3 squares, spanning 2 rows and 2 columns (rows 6–7, columns 1–2).

Amber occupies 4 squares within rows 1–2, columns 6–8.

Slate: 5 squares across rows 4–6, columns 3–5.

Pale yellow covers 7 squares, spanning 2 rows and 6 columns (rows 7–8, columns 1–6).

Khaki occupies 12 squares within rows 5–8, columns 4–8.

Blue: 14 squares across rows 1–6, columns 1–3.

Mint covers 17 squares, spanning 5 rows and 5 columns (rows 1–5, columns 4–8).

Where to start on this board

Open on the tightest color. Here that is indigo, confined to 2 squares between rows 1 and 2 and columns 2 and 2. Its queen has nowhere else to go, which means those 2 rows and 1 column carry more constraint than anywhere else on #129.

Because indigo stays inside column 2, its queen belongs to that column and no other region may use it. Cross out the rest of column 2 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.

Work outward to the other flat regions next. Amber, red 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 #129

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3 and 8 are the narrowest, touched by only 2 colors. Columns 1, 3, 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 6 meets 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.

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.

Keep alternating between two views of the board. In the region view you ask which of the eight colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 8x8 board unwinds.

A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.

Why puzzle #129 is rated medium

What earns a board its rating is the shape of its opening. Here that opening offers one single-line region, a 2-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 15. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

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.

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 #129 is row 3.

As a sanity check rather than a spoiler: the finished solution to #129 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.