12x12 Queens Puzzle #34
Difficulty: hard. 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 13-step reasoning is written out below.
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Step-by-step solution for puzzle #34
What follows is a complete solve of puzzle #34, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 12 queen placements and 1 elimination step 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 confined to one line.
Techniques this board needs: last square in a region, region confined to one line.
Show the full walkthrough (3 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: sea green has one square left, so its queen takes row 10, column 3; orange has one square left, so its queen takes row 9, column 5; teal has one square left, so its queen takes row 11, column 1; indigo has one square left, so its queen takes row 1, column 2; amber has one square left, so its queen takes row 2, column 11; red has one square left, so its queen takes row 6, 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 6, column 12.
Step 2. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 3 squares in all.
The board after step 2 — 6 of 12 queens placed. Step 3. 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: mint has one square left, so its queen takes row 4, column 9; slate has one square left, so its queen takes row 5, column 4; blue has one square left, so its queen takes row 3, column 7; pale yellow has one square left, so its queen takes row 7, column 6; rose has one square left, so its queen takes row 12, column 8; khaki has one square left, so its queen takes row 8, column 10. 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 8, column 10.
The board after step 3 — 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 #34
Board #34 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, #34 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 #34 are: sea green (1 square), red (4 squares), amber (5 squares), orange (6 squares), indigo (8 squares), teal (9 squares), mint (12 squares), blue (13 squares), rose (13 squares), pale yellow (17 squares), slate (26 squares), khaki (30 squares). An even split would hand every color 12 squares, so the sea green region is running 11 squares under that average while the khaki region is the roomiest area on the grid with 30 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 sea green, with 1 square, is under far more pressure than khaki with 30. A 29-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Sea green is the densest region on this grid at 100% of a 1×1 frame; slate is the loosest, occupying only 41% of its 8×8 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 #34, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Sea green covers 1 square, spanning 1 row and 1 column (rows 10–10, columns 3–3). It never leaves row 10, so its queen is locked to that row.
Red occupies 4 squares within rows 5–7, columns 11–12.
Amber: 5 squares across rows 1–2, columns 9–12.
Orange covers 6 squares, spanning 2 rows and 5 columns (rows 9–10, columns 4–8).
Indigo occupies 8 squares within rows 1–4, columns 1–3.
Teal: 9 squares across rows 9–11, columns 1–4.
Mint covers 12 squares, spanning 4 rows and 5 columns (rows 2–5, columns 8–12).
Blue occupies 13 squares within rows 1–3, columns 4–8.
Rose: 13 squares across rows 11–12, columns 1–9.
Pale yellow covers 17 squares, spanning 5 rows and 5 columns (rows 5–9, columns 4–8).
Slate occupies 26 squares within rows 2–9, columns 1–8.
Khaki: 30 squares across rows 4–12, columns 8–12.
Where to start on this board
Sea green is the natural opening on #34: it is the smallest region on the grid at 1 square, boxed into rows 10–10 and columns 3–3. 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 sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. 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. Amber, orange 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 #34
A quick way to find the next move is to count how many different colors touch each line. On this board, row 12 is the narrowest, touched by only 2 colors. Column 10 is the tightest column, with 3 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 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.
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 #34 is rated hard
The rating reflects how much the board concedes up front. Puzzle #34 has two 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 29 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.
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 #34, start hunting for it near row 12.
As a sanity check rather than a spoiler: the finished solution to #34 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.
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 #34?
Puzzle #34 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #34 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #34, 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 #34?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.