7x7 Queens Puzzle #209

About 7x7 Queens puzzle #209

Puzzle #209 is one of the medium-rated boards in the 7x7 set. Seven colors divide its 49 squares, and you win by placing seven 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, #209 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 #209 are: red (1 square), pale yellow (4 squares), indigo (6 squares), blue (6 squares), slate (8 squares), amber (10 squares), mint (14 squares). An even split would hand every color 7 squares, so the red region is running 6 squares under that average while the mint region is the roomiest area on the grid with 14 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Red has only 1 place to put its queen; mint has 14. The spread between them on this board is 13 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

Shape matters as much as size. The blue region is the most compact color here, filling 100% of the 3×2 box that encloses it, while mint is the most scattered at 50% of its 7×4 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 #209 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.

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

Pale yellow: 4 squares across rows 6–7, columns 6–7.

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

Blue occupies 6 squares within rows 1–3, columns 6–7.

Slate: 8 squares across rows 5–7, columns 1–4.

Amber covers 10 squares, spanning 4 rows and 4 columns (rows 2–5, columns 1–4).

Mint occupies 14 squares within rows 1–7, columns 4–7.

Where to start on this board

Red is the natural opening on #209: it is the smallest region on the grid at 1 square, boxed into rows 6–6 and columns 1–1. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.

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. Pale yellow is no more than two rows tall, so its queen is 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 #209

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

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 6 rows. Row 6, meeting 4 colors, is the opposite case — the busiest line on #209 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 seven colors looking for one with a single square left; sweep the seven rows and seven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 7x7 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 #209 is rated medium

What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 13. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

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 medium 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 7x7

At 7x7 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.

One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #209 the place to look for one is around column 5.

Here is a shape check that gives nothing away: when #209 is solved, 4 queens sit on the outer edge of the grid and 3 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.