12x12 Queens Puzzle #126
Difficulty: medium. Place 12 queens on this 12x12 board so that no two share a row, column or color region and none touch — including diagonally. This puzzle has exactly one solution, and it has been verified solvable by deduction alone: the complete 15-step reasoning is written out below.
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Step-by-step solution for puzzle #126
What follows is a complete solve of puzzle #126, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 12 queen placements and 3 elimination steps that narrow the board between them. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the region shadow.
Techniques this board needs: last square in a region, region confined to one line, region shadow.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Only row 1, column 9 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 9, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The rose region is down to one open square, at row 12, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 12 and column 4, the remaining rose squares, and the ring of neighbours around row 12, column 4.
Step 3. Only row 11, column 11 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 11, in teal and in the ring around that square is now dead.
The board after step 3 — 3 of 12 queens placed. Step 4. All of the slate region's remaining squares (5 open squares) lie in column 12. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 5. Only row 9, column 10 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 10, the rest of the orange region and every square adjacent to it — diagonals included.
Step 6. The pale yellow region is down to one open square, at row 7, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 8, the remaining pale yellow squares, and the ring of neighbours around row 7, column 8.
Step 7. Only row 2, column 7 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 7, in amber and in the ring around that square is now dead.
The board after step 7 — 6 of 12 queens placed. Step 8. Mint is down to 4 candidates in rows 4–6, columns 5 and 6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 9. Sea green cannot leave row 10 — every one of its open squares (2 open squares) sits there. That row belongs to sea green, so every square on it owned by another colour is dead: 3 squares in all.
Step 10. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: khaki has one square left, so its queen takes row 8, column 6; mint has one square left, so its queen takes row 4, column 5; red has one square left, so its queen takes row 6, column 3; sea green has one square left, so its queen takes row 10, column 1; blue has one square left, so its queen takes row 3, column 2; slate has one square left, so its queen takes row 5, column 12. After each one, clear that row, that column, the rest of the colour and the ring of neighbours before looking for the next. The last of them seats the queen on row 5, column 12.
The board after step 10 — 12 of 12 queens placed.
That completes the board: 12 queens seated, one in every row, one in every column and one in every colour, with no two of them touching. Notice that nothing in the sequence above required a guess — each placement followed from an elimination already on the grid, which is what “single solution, solvable by logic” actually means in practice.
About 12x12 Queens puzzle #126
Board #126 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, #126 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 #126 are: indigo (1 square), rose (1 square), teal (3 squares), pale yellow (6 squares), slate (8 squares), sea green (10 squares), blue (14 squares), mint (14 squares), khaki (19 squares), orange (20 squares), amber (21 squares), red (27 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the red region is the roomiest area on the grid with 27 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So indigo, with 1 square, is under far more pressure than red with 27. A 26-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×1 frame; pale yellow is the loosest, occupying only 50% of its 3×4 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 #126, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo: 1 square across rows 1–1, columns 9–9. It never leaves row 1, so its queen is locked to that row.
Rose covers 1 square, spanning 1 row and 1 column (rows 12–12, columns 4–4). It never leaves row 12, so its queen is locked to that row.
Teal occupies 3 squares within rows 11–12, columns 10–11.
Pale yellow: 6 squares across rows 6–8, columns 8–11.
Slate covers 8 squares, spanning 5 rows and 2 columns (rows 3–7, columns 11–12).
Sea green occupies 10 squares within rows 10–12, columns 1–4.
Blue: 14 squares across rows 1–6, columns 1–3.
Mint covers 14 squares, spanning 5 rows and 4 columns (rows 2–6, columns 5–8).
Khaki occupies 19 squares within rows 7–12, columns 4–8.
Orange: 20 squares across rows 8–12, columns 7–12.
Amber covers 21 squares, spanning 6 rows and 7 columns (rows 1–6, columns 6–12).
Red occupies 27 squares within rows 1–10, columns 1–5.
Where to start on this board
Indigo is the natural opening on #126: it is the smallest region on the grid at 1 square, boxed into rows 1–1 and columns 9–9. 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 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. 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 #126
A quick way to find the next move is to count how many different colors touch each line. On this board, row 9 is the narrowest, touched by only 3 colors. Columns 1, 2, 3, 5, 6 and 12 are the tightest columns, 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 6, meeting 6 colors, is the opposite case — the busiest line on #126 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.
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 #126 is rated medium
The rating reflects how much the board concedes up front. Puzzle #126 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 26 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #126, start hunting for it near row 9.
Here is a shape check that gives nothing away: when #126 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.
How to play Queens
- The board is an N×N grid divided into N colored regions.
- Place exactly one queen (♛) in each row, each column, and each colored region.
- No two queens may touch each other — not horizontally, vertically, or diagonally.
- Tap once to mark a square with an X (where a queen can't go), tap again to place a queen, and once more to clear it.
- There is always exactly one valid solution. Use logic, never guessing, to find it.
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Questions about this puzzle
How hard is 12x12 Queens puzzle #126?
Puzzle #126 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #126 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #126, has been verified to have exactly one valid arrangement of twelve queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #126?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.