12x12 Queens Puzzle #38

About 12x12 Queens puzzle #38

Board #38 of the 12x12 bank carries a hard rating. Its 144 squares are shared between twelve colored regions, and the solution places twelve queens: one per row, one per column, one per region, none of them side by side or corner to corner.

As with every puzzle in this collection, #38 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.

How the colors divide this board

From smallest to largest, the regions on puzzle #38 are: blue (1 square), rose (1 square), khaki (2 squares), orange (2 squares), amber (6 squares), slate (10 squares), pale yellow (11 squares), sea green (13 squares), red (14 squares), mint (19 squares), indigo (23 squares), teal (42 squares). An even split would hand every color 12 squares, so the blue region is running 11 squares under that average while the teal region is the roomiest area on the grid with 42 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Blue has only 1 place to put its queen; teal has 42. The spread between them on this board is 41 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

Look at arrangement as well as area. Blue is the densest region on this grid at 100% of a 1×1 frame; red is the loosest, occupying only 52% of its 9×3 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

Region by region

Here is the full footprint of every color on puzzle #38, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Blue occupies 1 square within rows 3–3, columns 8–8. It never leaves row 3, so its queen is locked to that row.

Rose: 1 square across rows 12–12, columns 2–2. It never leaves row 12, so its queen is locked to that row.

Khaki covers 2 squares, spanning 2 rows and 1 column (rows 7–8, columns 12–12). It sits wholly inside column 12, so its queen must be in that column.

Orange occupies 2 squares within rows 9–9, columns 7–8. It never leaves row 9, so its queen is locked to that row.

Amber: 6 squares across rows 1–4, columns 6–7.

Slate covers 10 squares, spanning 5 rows and 3 columns (rows 2–6, columns 1–3).

Pale yellow occupies 11 squares within rows 4–9, columns 8–10.

Sea green: 13 squares across rows 5–10, columns 1–4.

Red covers 14 squares, spanning 9 rows and 3 columns (rows 4–12, columns 10–12).

Mint occupies 19 squares within rows 1–6, columns 1–6.

Indigo: 23 squares across rows 1–7, columns 7–12.

Teal covers 42 squares, spanning 7 rows and 11 columns (rows 6–12, columns 1–11).

Where to start on this board

Blue is the natural opening on #38: it is the smallest region on the grid at 1 square, boxed into rows 3–3 and columns 8–8. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.

Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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. Orange, rose and khaki 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 #38

A quick way to find the next move is to count how many different colors touch each line. On this board, row 11 is the narrowest, touched by only 2 colors. Column 5 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 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 11 rows. By contrast row 6 meets 7 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.

Working through the middle game

The middle of #38 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.

Keep alternating between two views of the board. In the region view you ask which of the twelve 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 12x12 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 #38 is rated hard

The rating reflects how much the board concedes up front. Puzzle #38 has six regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 41 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.

A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.

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 #38 the place to look for one is around row 11.

As a sanity check rather than a spoiler: the finished solution to #38 puts 4 queens on the outer border and 8 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.