11x11 Queens Puzzle #215

About 11x11 Queens puzzle #215

11x11 puzzle #215 is rated easy. Eleven colored regions cover its 121 squares, and your job is to seat eleven queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.

Puzzle #215 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 #215 are: teal (1 square), slate (2 squares), indigo (3 squares), amber (3 squares), sea green (7 squares), blue (10 squares), khaki (10 squares), orange (15 squares), mint (18 squares), pale yellow (21 squares), red (31 squares). An even split would hand every color 11 squares, so the teal region is running 10 squares under that average while the red region is the roomiest area on the grid with 31 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Teal has only 1 place to put its queen; red has 31. The spread between them on this board is 30 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

A region's outline can constrain it more than its size does. Here slate is the most solid, filling 100% of its 2×1 box, and mint the most diffuse at 43% of its 6×7 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 #215, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Teal occupies 1 square within rows 11–11, columns 11–11. It never leaves row 11, so its queen is locked to that row.

Slate: 2 squares across rows 5–6, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.

Indigo covers 3 squares, spanning 2 rows and 2 columns (rows 1–2, columns 10–11).

Amber occupies 3 squares within rows 1–2, columns 5–6.

Sea green: 7 squares across rows 8–11, columns 1–3.

Blue covers 10 squares, spanning 3 rows and 5 columns (rows 1–3, columns 1–5).

Khaki occupies 10 squares within rows 8–11, columns 2–5.

Orange: 15 squares across rows 8–11, columns 5–11.

Mint covers 18 squares, spanning 6 rows and 7 columns (rows 1–6, columns 4–10).

Pale yellow occupies 21 squares within rows 2–8, columns 1–5.

Red: 31 squares across rows 3–10, columns 6–11.

Where to start on this board

The most constrained color is where a solve should begin, and on #215 that is teal with 1 square. It reaches from row 11 to row 11 and from column 11 to column 11 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.

Because teal never leaves row 11, its queen must be in that row — and that instantly settles row 11 for everyone else. Sweep along it and X out every square that is not teal. 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. Amber, indigo and slate 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 #215

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 2 colors. Columns 7, 8 and 9 are the tightest columns, with 3 colors.

Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 8 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

The middle of #215 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.

Keep alternating between two views of the board. In the region view you ask which of the eleven 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 11x11 board unwinds.

The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.

Why puzzle #215 is rated easy

The rating reflects how much the board concedes up front. Puzzle #215 has three regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 30 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.

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.

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 #215 the place to look for one is around row 7.

As a sanity check rather than a spoiler: the finished solution to #215 puts 3 queens on the outer border and 8 queens in the interior, 1 of them in an actual 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.