9x9 Queens Puzzle #206

About 9x9 Queens puzzle #206

Board #206 of the 9x9 bank carries a medium rating. Its 81 squares are shared between nine colored regions, and the solution places nine queens: one per row, one per column, one per region, none of them side by side or corner to corner.

As with every puzzle in this collection, #206 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 #206 are: slate (1 square), orange (2 squares), pale yellow (3 squares), indigo (7 squares), blue (7 squares), mint (9 squares), amber (16 squares), khaki (17 squares), red (19 squares). An even split would hand every color 9 squares, so the slate region is running 8 squares under that average while the red region is the roomiest area on the grid with 19 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 slate, with 1 square, is under far more pressure than red with 19. A 18-square gap like this one rewards players who start where the choices are fewest.

Shape matters as much as size. The slate region is the most compact color here, filling 100% of the 1×1 box that encloses it, while red is the most scattered at 45% of its 6×7 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.

Region by region

Below is every color on #206 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.

Slate occupies 1 square within rows 5–5, columns 9–9. It never leaves row 5, so its queen is locked to that row.

Orange: 2 squares across rows 8–9, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.

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

Indigo occupies 7 squares within rows 1–4, columns 7–9.

Blue: 7 squares across rows 3–4, columns 3–7.

Mint covers 9 squares, spanning 3 rows and 4 columns (rows 3–5, columns 1–4).

Amber occupies 16 squares within rows 1–3, columns 1–8.

Khaki: 17 squares across rows 6–9, columns 5–9.

Red covers 19 squares, spanning 6 rows and 7 columns (rows 4–9, columns 2–8).

Where to start on this board

Open on the tightest color. Here that is slate, confined to 1 square between rows 5 and 5 and columns 9 and 9. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #206.

Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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. Blue, pale yellow and orange 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 #206

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 2 are the narrowest, touched by only 2 colors. Column 9 is the tightest column, with 3 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 8 rows. Row 4, meeting 4 colors, is the opposite case — the busiest line on #206 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 nine colors looking for one with a single square left; sweep the nine rows and nine columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 9x9 solve from a stalled one.

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 #206 is rated medium

What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 18. 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 9x9

At 9x9 a full re-scan after every move starts to get slow, so work locally instead. Once a queen goes down, check only the regions, rows and columns that placement actually touched — that is where new information appeared. Fall back to a complete sweep only when the local pass turns up nothing, and your solve times will drop noticeably.

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 #206, start hunting for it near row 1.

Here is a shape check that gives nothing away: when #206 is solved, 3 queens sit on the outer edge of the grid and 6 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.