12x12 Queens Puzzle #211

About 12x12 Queens puzzle #211

12x12 puzzle #211 is rated medium. Twelve colored regions cover its 144 squares, and your job is to seat twelve queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.

Puzzle #211 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 #211 are: pale yellow (1 square), indigo (2 squares), khaki (3 squares), teal (3 squares), mint (5 squares), rose (10 squares), orange (11 squares), slate (14 squares), blue (20 squares), sea green (20 squares), amber (23 squares), red (32 squares). An even split would hand every color 12 squares, so the pale yellow region is running 11 squares under that average while the red region is the roomiest area on the grid with 32 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 red has 32 to spare, a gap of 31. 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 indigo is the most solid, filling 100% of its 1×2 box, and slate the most diffuse at 47% of its 5×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.

Pale yellow covers 1 square, spanning 1 row and 1 column (rows 7–7, columns 10–10). It never leaves row 7, so its queen is locked to that row.

Indigo occupies 2 squares within rows 1–1, columns 6–7. It never leaves row 1, so its queen is locked to that row.

Khaki: 3 squares across rows 7–8, columns 1–2.

Teal covers 3 squares, spanning 2 rows and 2 columns (rows 11–12, columns 10–11).

Mint occupies 5 squares within rows 4–6, columns 6–8.

Rose: 10 squares across rows 8–12, columns 1–3.

Orange covers 11 squares, spanning 5 rows and 3 columns (rows 8–12, columns 10–12).

Slate occupies 14 squares within rows 3–7, columns 1–6.

Blue: 20 squares across rows 1–5, columns 1–6.

Sea green covers 20 squares, spanning 6 rows and 6 columns (rows 7–12, columns 2–7).

Amber occupies 23 squares within rows 1–5, columns 5–12.

Red: 32 squares across rows 4–12, columns 6–12.

Where to start on this board

Begin where the choices are fewest. On this board that means pale yellow, which owns just 1 square inside a 1×1 window running from row 7 to row 7 and column 10 to column 10. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

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. Indigo, khaki and teal 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 #211

A quick way to find the next move is to count how many different colors touch each line. On this board, row 2 is the narrowest, touched by only 2 colors. Column 9 is the tightest column, with 2 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 11 rows. Row 12, meeting 5 colors, is the opposite case — the busiest line on #211 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.

With twelve queens to seat and twelve regions competing over 144 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 12x12 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 #211 is rated medium

Ratings track how generous the opening is. On #211 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 31-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.

The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a medium board from the rest.

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 12x12

At 12x12 you are managing 144 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 row 2 on this board.

Here is a shape check that gives nothing away: when #211 is solved, 4 queens sit on the outer edge of the grid and 8 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.