12x12 Queens Puzzle #212

About 12x12 Queens puzzle #212

This is puzzle number 212 in the 12x12 collection, rated easy. The grid holds 144 squares split between twelve colored regions, and a finished board carries twelve queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.

Puzzle #212 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 #212 are: indigo (1 square), pale yellow (1 square), khaki (6 squares), rose (6 squares), amber (9 squares), blue (10 squares), red (13 squares), mint (15 squares), orange (16 squares), teal (16 squares), sea green (19 squares), slate (32 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the slate region is the roomiest area on the grid with 32 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 1 place to put its queen; slate has 32. The spread between them on this board is 31 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 #212, packing 100% of its 1×1 bounding box, whereas red straggles across its 6×6 box at just 36%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

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.

Indigo occupies 1 square within rows 1–1, columns 12–12. It never leaves row 1, so its queen is locked to that row.

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

Khaki covers 6 squares, spanning 3 rows and 3 columns (rows 7–9, columns 10–12).

Rose occupies 6 squares within rows 11–12, columns 5–9.

Amber: 9 squares across rows 1–2, columns 1–8.

Blue covers 10 squares, spanning 4 rows and 3 columns (rows 2–5, columns 1–3).

Red occupies 13 squares within rows 4–9, columns 6–11.

Mint: 15 squares across rows 1–6, columns 9–12.

Orange covers 16 squares, spanning 5 rows and 7 columns (rows 7–11, columns 1–7).

Teal occupies 16 squares within rows 9–12, columns 1–4.

Sea green: 19 squares across rows 8–12, columns 6–12.

Slate covers 32 squares, spanning 6 rows and 10 columns (rows 2–7, columns 1–10).

Where to start on this board

The most constrained color is where a solve should begin, and on #212 that is indigo with 1 square. It reaches from row 1 to row 1 and from column 12 to column 12 — 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 indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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, amber and rose 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 #212

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3, 6, 10 and 12 are the narrowest, touched by only 3 colors. Columns 4, 5, 11 and 12 are the tightest columns, with 4 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 11 rows. By contrast row 9 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.

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.

Resist the plausible-looking queen. On #212 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.

Why puzzle #212 is rated easy

Ratings track how generous the opening is. On #212 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 31-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.

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.

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.

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 #212 the place to look for one is around row 1.

As a sanity check rather than a spoiler: the finished solution to #212 puts 3 queens on the outer border and 9 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.