12x12 Queens Puzzle #130
Difficulty: easy. 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 22-step reasoning is written out below.
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Step-by-step solution for puzzle #130
What follows is a complete solve of puzzle #130, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 12 queen placements and 10 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 pairing argument on rows.
Techniques this board needs: last square in a region, region shadow, pairing argument on rows, region confined to one line, line confined to one region, last square in a column.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 11, column 8 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 8, the rest of the teal region and every square adjacent to it — diagonals included.
Step 2. The rose region is down to one open square, at row 12, column 12. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 12 and column 12, the remaining rose squares, and the ring of neighbours around row 12, column 12.
Step 3. The slate region has 3 squares left, spread across rows 5 and 8, columns 10 and 11. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 4. Wherever red ends up among its 3 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
Step 5. Pale yellow is down to 5 candidates in rows 6–8, columns 1–3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
The board after step 5 — 2 of 12 queens placed. Step 6. Here is the pairing argument. The khaki, orange, and sea green regions have no open squares outside rows 8–10 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 8 squares come off in one stroke.
Step 7. Only row 5, column 11 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 11, in slate and in the ring around that square is now dead.
Step 8. Mint is down to 4 candidates in rows 3 and 4, columns 1–3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about mint itself.
Step 9. Red cannot leave row 6 — every one of its open squares (2 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 6 squares in all.
The board after step 9 — 3 of 12 queens placed. Step 10. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 11. Orange cannot leave column 10 — every one of its open squares (2 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 4 squares in all.
Step 12. Every open square left in column 9 (4 open squares) belongs to the amber region. Since that column must contain a queen, amber is the colour that supplies it — so amber squares anywhere else on the board are out, 3 squares in all.
Step 13. Column 7 has only blue squares left (2 open squares). The column needs a queen and only blue can provide one, which pins that colour to this column and kills its squares elsewhere: 8 squares.
Step 14. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: column 6 is down to one square, putting a queen on row 10, column 6; orange has one square left, so its queen takes row 9, column 10; khaki has one square left, so its queen takes row 8, column 1; pale yellow has one square left, so its queen takes row 7, column 3; mint has one square left, so its queen takes row 4, column 2; blue has one square left, so its queen takes row 3, column 7; red has one square left, so its queen takes row 6, column 5; indigo has one square left, so its queen takes row 1, column 4; amber has one square left, so its queen takes row 2, column 9. 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 2, column 9.
The board after step 14 — 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 #130
Board #130 of the 12x12 bank carries a easy 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, #130 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 #130 are: teal (1 square), rose (2 squares), red (3 squares), pale yellow (6 squares), mint (7 squares), indigo (10 squares), slate (10 squares), khaki (10 squares), orange (12 squares), sea green (26 squares), amber (27 squares), blue (30 squares). An even split would hand every color 12 squares, so the teal region is running 11 squares under that average while the blue 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 teal, with 1 square, is under far more pressure than blue with 30. A 29-square gap like this one rewards players who start where the choices are fewest.
A region's outline can constrain it more than its size does. Here teal is the most solid, filling 100% of its 1×1 box, and slate the most diffuse at 48% of its 7×3 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Here is the full footprint of every color on puzzle #130, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Teal covers 1 square, spanning 1 row and 1 column (rows 11–11, columns 8–8). It never leaves row 11, so its queen is locked to that row.
Rose occupies 2 squares within rows 11–12, columns 12–12. It sits wholly inside column 12, so its queen must be in that column.
Red: 3 squares across rows 5–6, columns 4–5.
Pale yellow covers 6 squares, spanning 3 rows and 3 columns (rows 6–8, columns 1–3).
Mint occupies 7 squares within rows 3–5, columns 1–3.
Indigo: 10 squares across rows 1–3, columns 1–5.
Slate covers 10 squares, spanning 7 rows and 3 columns (rows 3–9, columns 10–12).
Khaki occupies 10 squares within rows 7–11, columns 1–3.
Orange: 12 squares across rows 9–12, columns 9–12.
Sea green covers 26 squares, spanning 6 rows and 9 columns (rows 7–12, columns 1–9).
Amber occupies 27 squares within rows 1–7, columns 6–12.
Blue: 30 squares across rows 2–9, columns 4–9.
Where to start on this board
Teal is the natural opening on #130: it is the smallest region on the grid at 1 square, boxed into rows 11–11 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 teal never leaves row 11, its queen must be in that row — and that instantly settles row 11 for everyone else. Sweep along it and X out every square that is not teal. 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. Red 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 #130
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Columns 6, 7, 10 and 11 are the tightest columns, 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 7 meets 6 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 #130 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.
The whole middle game reduces to two sweeps. Sweep the twelve colors looking for one with a single square left; sweep the twelve rows and twelve columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 12x12 solve from a stalled one.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #130 is rated easy
The rating reflects how much the board concedes up front. Puzzle #130 has three 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 #130, start hunting for it near row 1.
As a sanity check rather than a spoiler: the finished solution to #130 puts 3 queens on the outer border and 9 queens in the interior, 1 of them in an actual 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 #130?
Puzzle #130 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #130 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #130, 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 #130?
Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.