11x11 Queens Puzzle #210

About 11x11 Queens puzzle #210

Board #210 of the 11x11 bank carries a medium rating. Its 121 squares are shared between eleven colored regions, and the solution places eleven queens: one per row, one per column, one per region, none of them side by side or corner to corner.

Like every board on this site, #210 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 #210 are: mint (1 square), teal (1 square), red (5 squares), indigo (6 squares), amber (10 squares), blue (11 squares), sea green (11 squares), khaki (15 squares), orange (15 squares), pale yellow (16 squares), slate (30 squares). An even split would hand every color 11 squares, so the mint region is running 10 squares under that average while the slate region is the roomiest area on the grid with 30 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Mint has only 1 place to put its queen; slate has 30. The spread between them on this board is 29 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #210, packing 100% of its 2×3 bounding box, whereas blue straggles across its 5×5 box at just 44%. 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 #210, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Mint: 1 square across rows 4–4, columns 11–11. It never leaves row 4, so its queen is locked to that row.

Teal covers 1 square, spanning 1 row and 1 column (rows 11–11, columns 2–2). It never leaves row 11, so its queen is locked to that row.

Red occupies 5 squares within rows 4–6, columns 2–4.

Indigo: 6 squares across rows 1–2, columns 9–11.

Amber covers 10 squares, spanning 4 rows and 3 columns (rows 1–4, columns 1–3).

Blue occupies 11 squares within rows 3–7, columns 7–11.

Sea green: 11 squares across rows 7–11, columns 3–6.

Khaki covers 15 squares, spanning 7 rows and 3 columns (rows 5–11, columns 1–3).

Orange occupies 15 squares within rows 8–11, columns 5–11.

Pale yellow: 16 squares across rows 6–10, columns 7–11.

Slate covers 30 squares, spanning 8 rows and 7 columns (rows 1–8, columns 3–9).

Where to start on this board

Begin where the choices are fewest. On this board that means mint, which owns just 1 square inside a 1×1 window running from row 4 to row 4 and column 11 to column 11. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Because mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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. Teal 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 #210

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

After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.

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 #210 is rated medium

The rating reflects how much the board concedes up front. Puzzle #210 has four 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 29 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.

If #210 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 #210 the place to look for one is around column 1.

As a sanity check rather than a spoiler: the finished solution to #210 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.