11x11 Queens Puzzle #260

About 11x11 Queens puzzle #260

This is puzzle number 260 in the 11x11 collection, rated easy. The grid holds 121 squares split between eleven colored regions, and a finished board carries eleven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.

Puzzle #260 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.

How the colors divide this board

From smallest to largest, the regions on puzzle #260 are: indigo (1 square), orange (1 square), khaki (4 squares), red (7 squares), teal (7 squares), mint (9 squares), pale yellow (12 squares), sea green (14 squares), slate (15 squares), amber (23 squares), blue (28 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the blue region is the roomiest area on the grid with 28 squares.

Every color takes one queen and one only, whatever its size — which is why the 27 square difference between indigo and blue 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.

A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and mint the most diffuse at 43% of its 7×3 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

Here is the full footprint of every color on puzzle #260, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

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

Orange: 1 square across rows 9–9, columns 1–1. It never leaves row 9, so its queen is locked to that row.

Khaki covers 4 squares, spanning 4 rows and 1 column (rows 8–11, columns 11–11). It sits wholly inside column 11, so its queen must be in that column.

Red occupies 7 squares within rows 6–8, columns 4–7.

Teal: 7 squares across rows 10–11, columns 4–9.

Mint covers 9 squares, spanning 7 rows and 3 columns (rows 1–7, columns 9–11).

Pale yellow occupies 12 squares within rows 7–11, columns 7–10.

Sea green: 14 squares across rows 8–11, columns 1–7.

Slate covers 15 squares, spanning 6 rows and 4 columns (rows 4–9, columns 1–4).

Amber occupies 23 squares within rows 1–7, columns 7–10.

Blue: 28 squares across rows 1–6, columns 1–7.

Where to start on this board

Open on the tightest color. Here that is indigo, confined to 1 square between rows 1 and 1 and columns 6 and 6. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #260.

Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Orange and teal 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 #260

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2 and 3 are the narrowest, touched by only 3 colors. Column 11 is the tightest column, with 2 colors.

Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 9 meets 5 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.

Two checks, run alternately, will carry you through the 121 squares of this grid. First: has any of the eleven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 11x11 boards almost always run one of those checks and forget the other.

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 #260 is rated easy

The rating reflects how much the board concedes up front. Puzzle #260 has five regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 27 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.

When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.

Techniques that work well at 11x11

At 11x11 you are managing 121 squares, and holding the whole board in your head will not work. Split it into quadrants and solve locally. Most useful deductions on a grid this large are regional — a color pinched between two placed queens, or a band of rows that two regions must share. Trust the marks on the board over your memory.

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 #260 is column 11.

As a sanity check rather than a spoiler: the finished solution to #260 puts 4 queens on the outer border and 7 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.