12x12 Queens Puzzle #122

About 12x12 Queens puzzle #122

Board #122 of the 12x12 bank carries a medium 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, #122 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 #122 are: pale yellow (1 square), rose (1 square), amber (3 squares), blue (3 squares), indigo (5 squares), sea green (9 squares), slate (12 squares), orange (12 squares), teal (18 squares), red (22 squares), khaki (26 squares), mint (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 mint 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. Pale yellow has only 1 place to put its queen; mint 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.

Look at arrangement as well as area. Pale yellow is the densest region on this grid at 100% of a 1×1 frame; khaki is the loosest, occupying only 58% of its 5×9 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 #122, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Pale yellow occupies 1 square within rows 7–7, columns 12–12. It never leaves row 7, so its queen is locked to that row.

Rose: 1 square across rows 12–12, columns 10–10. It never leaves row 12, so its queen is locked to that row.

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

Blue occupies 3 squares within rows 3–4, columns 3–4.

Indigo: 5 squares across rows 1–2, columns 9–12.

Sea green covers 9 squares, spanning 5 rows and 3 columns (rows 8–12, columns 10–12).

Slate occupies 12 squares within rows 5–8, columns 8–12.

Orange: 12 squares across rows 8–12, columns 1–4.

Teal covers 18 squares, spanning 3 rows and 9 columns (rows 10–12, columns 3–11).

Red occupies 22 squares within rows 1–9, columns 1–4.

Khaki: 26 squares across rows 6–10, columns 3–11.

Mint covers 32 squares, spanning 5 rows and 10 columns (rows 1–5, columns 3–12).

Where to start on this board

Pale yellow is the natural opening on #122: it is the smallest region on the grid at 1 square, boxed into rows 7–7 and columns 12–12. 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 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. Rose, amber, indigo and blue 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 #122

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3, 4, 5, 6 and 11 are the narrowest, touched by only 3 colors. Columns 1 and 2 are the tightest columns, with 2 colors.

Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 11 rows. Row 8 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.

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.

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.

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 #122 is rated medium

The rating reflects how much the board concedes up front. Puzzle #122 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 31 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.

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 #122 the place to look for one is around column 1.

Use this as a rough check on your progress: the completed board has 4 queens around the border and 8 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.