11x11 Queens Puzzle #207

About 11x11 Queens puzzle #207

11x11 puzzle #207 is rated medium. 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, #207 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 #207 are: pale yellow (1 square), sea green (2 squares), indigo (3 squares), amber (3 squares), teal (7 squares), mint (8 squares), red (13 squares), orange (14 squares), blue (19 squares), slate (20 squares), khaki (31 squares). An even split would hand every color 11 squares, so the pale yellow region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 31 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Pale yellow is working with 1 square while khaki has 31 to spare, a gap of 30. Attack the cramped end and the roomy regions tend to resolve themselves.

A region's outline can constrain it more than its size does. Here pale yellow is the most solid, filling 100% of its 1×1 box, and mint the most diffuse at 53% of its 5×3 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

Below is every color on #207 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.

Pale yellow: 1 square across rows 7–7, columns 6–6. It never leaves row 7, so its queen is locked to that row.

Sea green covers 2 squares, spanning 1 row and 2 columns (rows 10–10, columns 7–8). It never leaves row 10, so its queen is locked to that row.

Indigo occupies 3 squares within rows 1–2, columns 10–11.

Amber: 3 squares across rows 1–2, columns 6–7.

Teal covers 7 squares, spanning 3 rows and 4 columns (rows 9–11, columns 5–8).

Mint occupies 8 squares within rows 2–6, columns 4–6.

Red: 13 squares across rows 5–9, columns 1–4.

Orange covers 14 squares, spanning 5 rows and 5 columns (rows 7–11, columns 1–5).

Blue occupies 19 squares within rows 1–6, columns 1–5.

Slate: 20 squares across rows 1–7, columns 6–10.

Khaki covers 31 squares, spanning 9 rows and 6 columns (rows 3–11, columns 6–11).

Where to start on this board

The most constrained color is where a solve should begin, and on #207 that is pale yellow with 1 square. It reaches from row 7 to row 7 and from column 6 to column 6 — 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 pale yellow never leaves row 7, its queen must be in that row — and that instantly settles row 7 for everyone else. Sweep along it and X out every square that is not pale yellow. 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. Sea green, amber and indigo 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 #207

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 8 and 11 are the narrowest, touched by only 3 colors. Columns 9 and 11 are the tightest columns, 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 7 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.

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.

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 #207 is rated medium

What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 30. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

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.

If #207 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.

Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around column 9 on this board.

As a sanity check rather than a spoiler: the finished solution to #207 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.