8x8 Queens Puzzle #133

About 8x8 Queens puzzle #133

Puzzle #133 is one of the easy-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, #133 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 #133 are: mint (1 square), blue (2 squares), khaki (3 squares), indigo (4 squares), pale yellow (4 squares), slate (13 squares), amber (15 squares), red (22 squares). An even split would hand every color 8 squares, so the mint region is running 7 squares under that average while the red region is the roomiest area on the grid with 22 squares.

Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So mint, with 1 square, is under far more pressure than red with 22. A 21-square gap like this one rewards players who start where the choices are fewest.

Look at arrangement as well as area. Blue is the densest region on this grid at 100% of a 2×1 frame; indigo is the loosest, occupying only 67% of its 3×2 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

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 5–5). It never leaves row 4, so its queen is locked to that row.

Blue occupies 2 squares within rows 2–3, columns 7–7. It sits wholly inside column 7, so its queen must be in that column.

Khaki: 3 squares across rows 8–8, columns 3–5. It never leaves row 8, so its queen is locked to that row.

Indigo covers 4 squares, spanning 3 rows and 2 columns (rows 1–3, columns 7–8).

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

Slate: 13 squares across rows 1–6, columns 1–3.

Amber covers 15 squares, spanning 4 rows and 5 columns (rows 1–4, columns 2–6).

Red occupies 22 squares within rows 4–8, columns 3–8.

Where to start on this board

Open on the tightest color. Here that is mint, confined to 1 square between rows 4 and 4 and columns 5 and 5. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #133.

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. Khaki, 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 #133

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5, 6 and 7 are the narrowest, touched by only 2 colors. Columns 1, 6 and 8 are the tightest columns, 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 4, meeting 4 colors, is the opposite case — the busiest line on #133 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.

Two checks, run alternately, will carry you through the 64 squares of this grid. First: has any of the eight regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 8x8 boards almost always run one of those checks and forget the other.

Resist the plausible-looking queen. On #133 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 #133 is rated easy

Ratings track how generous the opening is. On #133 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 21-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.

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.

Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #133, start hunting for it near row 5.

Here is a shape check that gives nothing away: when #133 is solved, 3 queens sit on the outer edge of the grid and 5 sit inside it, with 1 queen in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.