7x7 Queens Puzzle #278

About 7x7 Queens puzzle #278

Board #278 of the 7x7 bank carries a hard rating. Its 49 squares are shared between seven colored regions, and the solution places seven 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, #278 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 #278 are: red (1 square), slate (4 squares), indigo (5 squares), blue (6 squares), amber (7 squares), mint (7 squares), pale yellow (19 squares). An even split would hand every color 7 squares, so the red region is running 6 squares under that average while the pale yellow 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 red, with 1 square, is under far more pressure than pale yellow with 19. A 18-square gap like this one rewards players who start where the choices are fewest.

Square count is only half the story — how a color is arranged counts too. Red is the tidiest shape on #278, packing 100% of its 1×1 bounding box, whereas mint straggles across its 3×4 box at just 58%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Here is the full footprint of every color on puzzle #278, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Red occupies 1 square within rows 6–6, columns 7–7. It never leaves row 6, so its queen is locked to that row.

Slate: 4 squares across rows 4–6, columns 1–2.

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

Blue occupies 6 squares within rows 1–3, columns 2–4.

Amber: 7 squares across rows 1–3, columns 5–7.

Mint covers 7 squares, spanning 3 rows and 4 columns (rows 3–5, columns 3–6).

Pale yellow occupies 19 squares within rows 4–7, columns 1–7.

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 7 to column 7. 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.

No region here is pinned to a shallow band of rows, so turn the same idea sideways: indigo and slate span only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.

The tightest lines on puzzle #278

A quick way to find the next move is to count how many different colors touch each line. On this board, row 7 is the narrowest, touched by only 1 color. Columns 1, 3, 4, 5, 6 and 7 are the tightest columns, with 3 colors.

The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 1 color has to be claimed by one of them, which pushes every remaining region into the other 6 rows. Row 3, meeting 4 colors, is the opposite case — the busiest line on #278 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.

Keep alternating between two views of the board. In the region view you ask which of the seven 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 7x7 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 #278 is rated hard

The rating reflects how much the board concedes up front. Puzzle #278 has two regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 1 color, and the gap between its largest and smallest regions is 18 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

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 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.

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 #278, start hunting for it near row 7.

Here is a shape check that gives nothing away: when #278 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.