12x12 Queens Puzzle #159

About 12x12 Queens puzzle #159

12x12 puzzle #159 is rated easy. 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.

Like every board on this site, #159 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 #159 are: pale yellow (1 square), orange (2 squares), teal (3 squares), blue (5 squares), amber (7 squares), rose (8 squares), sea green (11 squares), mint (18 squares), red (19 squares), indigo (22 squares), slate (24 squares), khaki (24 squares). An even split would hand every color 12 squares, so the pale yellow region is running 11 squares under that average while the khaki region is the roomiest area on the grid with 24 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Pale yellow has only 1 place to put its queen; khaki has 24. The spread between them on this board is 23 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

A region's outline can constrain it more than its size does. Here pale yellow is the most solid, filling 100% of its 1×1 box, and indigo the most diffuse at 46% of its 6×8 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: 1 square across rows 7–7, columns 8–8. It never leaves row 7, so its queen is locked to that row.

Orange covers 2 squares, spanning 2 rows and 1 column (rows 9–10, columns 5–5). It sits wholly inside column 5, so its queen must be in that column.

Teal occupies 3 squares within rows 11–12, columns 11–12.

Blue: 5 squares across rows 3–5, columns 1–3.

Amber covers 7 squares, spanning 5 rows and 2 columns (rows 1–5, columns 11–12).

Rose occupies 8 squares within rows 11–12, columns 5–10.

Sea green: 11 squares across rows 10–12, columns 1–4.

Mint covers 18 squares, spanning 5 rows and 6 columns (rows 1–5, columns 6–11).

Red occupies 19 squares within rows 3–10, columns 1–4.

Indigo: 22 squares across rows 1–6, columns 1–8.

Slate covers 24 squares, spanning 5 rows and 8 columns (rows 5–9, columns 4–11).

Khaki occupies 24 squares within rows 6–11, 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 8 to column 8. 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. Orange, rose 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 #159

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 8 and 12 are the narrowest, touched by only 3 colors. Column 12 is the tightest column, with 3 colors.

The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 11 rows. Row 5, meeting 6 colors, is the opposite case — the busiest line on #159 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.

Resist the plausible-looking queen. On #159 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 #159 is rated easy

Ratings track how generous the opening is. On #159 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 23-square gap between the largest and smallest regions. Those four numbers largely explain the easy 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 easy board from the rest.

If #159 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 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 #159 the place to look for one is around row 1.

Here is a shape check that gives nothing away: when #159 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.