11x11 Queens Puzzle #202

About 11x11 Queens puzzle #202

Board #202 of the 11x11 bank carries a easy 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, #202 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 #202 are: mint (1 square), khaki (1 square), blue (2 squares), sea green (6 squares), red (7 squares), pale yellow (10 squares), orange (14 squares), teal (14 squares), indigo (19 squares), slate (20 squares), amber (27 squares). An even split would hand every color 11 squares, so the mint region is running 10 squares under that average while the amber region is the roomiest area on the grid with 27 squares.

Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So mint, with 1 square, is under far more pressure than amber with 27. A 26-square gap like this one rewards players who start where the choices are fewest.

Square count is only half the story — how a color is arranged counts too. Blue is the tidiest shape on #202, packing 100% of its 2×1 bounding box, whereas teal straggles across its 5×6 box at just 47%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a easy board.

Mint covers 1 square, spanning 1 row and 1 column (rows 4–4, columns 1–1). It never leaves row 4, so its queen is locked to that row.

Khaki occupies 1 square within rows 8–8, columns 11–11. It never leaves row 8, so its queen is locked to that row.

Blue: 2 squares across rows 3–4, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.

Sea green covers 6 squares, spanning 2 rows and 4 columns (rows 10–11, columns 8–11).

Red occupies 7 squares within rows 5–8, columns 1–2.

Pale yellow: 10 squares across rows 7–10, columns 5–9.

Orange covers 14 squares, spanning 6 rows and 4 columns (rows 6–11, columns 1–4).

Teal occupies 14 squares within rows 7–11, columns 3–8.

Indigo: 19 squares across rows 1–3, columns 3–11.

Slate covers 20 squares, spanning 8 rows and 5 columns (rows 3–10, columns 7–11).

Amber occupies 27 squares within rows 1–7, columns 1–8.

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 1 to column 1. 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. Khaki, blue and sea green 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 #202

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

The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 8, meeting 6 colors, is the opposite case — the busiest line on #202 and the last one you should expect to crack.

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.

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 #202 is rated easy

The easy label comes out of four measurable things about #202: five of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 26. Boards that score tight on those measures give up their first queen fast.

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 #202 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.

Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #202, start hunting for it near row 1.

Here is a shape check that gives nothing away: when #202 is solved, 4 queens sit on the outer edge of the grid and 7 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.