11x11 Queens Puzzle #27

About 11x11 Queens puzzle #27

11x11 puzzle #27 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.

Like every board on this site, #27 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.

How the colors divide this board

From smallest to largest, the regions on puzzle #27 are: amber (1 square), orange (1 square), pale yellow (4 squares), red (7 squares), mint (9 squares), khaki (9 squares), blue (13 squares), indigo (14 squares), teal (14 squares), sea green (23 squares), slate (26 squares). An even split would hand every color 11 squares, so the amber region is running 10 squares under that average while the slate region is the roomiest area on the grid with 26 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Amber has only 1 place to put its queen; slate has 26. The spread between them on this board is 25 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

Look at arrangement as well as area. Amber is the densest region on this grid at 100% of a 1×1 frame; indigo is the loosest, occupying only 50% of its 7×4 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

Region by region

Here is the full footprint of every color on puzzle #27, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Amber: 1 square across rows 2–2, columns 11–11. It never leaves row 2, so its queen is locked to that row.

Orange covers 1 square, spanning 1 row and 1 column (rows 9–9, columns 2–2). It never leaves row 9, so its queen is locked to that row.

Pale yellow occupies 4 squares within rows 7–7, columns 7–10. It never leaves row 7, so its queen is locked to that row.

Red: 7 squares across rows 5–8, columns 1–3.

Mint covers 9 squares, spanning 5 rows and 2 columns (rows 1–5, columns 1–2).

Khaki occupies 9 squares within rows 7–9, columns 3–7.

Blue: 13 squares across rows 1–3, columns 3–8.

Indigo covers 14 squares, spanning 7 rows and 4 columns (rows 1–7, columns 8–11).

Teal occupies 14 squares within rows 8–11, columns 7–11.

Sea green: 23 squares across rows 8–11, columns 1–10.

Slate covers 26 squares, spanning 4 rows and 8 columns (rows 3–6, columns 3–10).

Where to start on this board

The most constrained color is where a solve should begin, and on #27 that is amber with 1 square. It reaches from row 2 to row 2 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 amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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 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 #27

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 10 and 11 are the narrowest, touched by only 2 colors. Columns 1 and 11 are the tightest columns, with 3 colors.

A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 9 is the crowded extreme at 4 colors — worth revisiting later, not now.

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.

With eleven queens to seat and eleven regions competing over 121 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 11x11 boards quickly and players who stall halfway.

Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.

Why puzzle #27 is rated easy

The rating reflects how much the board concedes up front. Puzzle #27 has five 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 25 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.

If #27 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.

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 #27 the place to look for one is around row 10.

A non-spoiling distribution check: solved, #27 carries 4 queens on the perimeter against 7 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.