12x12 Queens Puzzle #129
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #129
What follows is a complete solve of puzzle #129, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 12 queen placements and 7 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: region shadow, region confined to one line, last square in a region, pairing argument on rows, last square in a column, last square in a row.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Wherever mint ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. Slate is down to 6 candidates in rows 5–7, columns 5–8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
Step 3. Sea green cannot leave column 9 — every one of its open squares (2 open squares) sits there. That column belongs to sea green, so every square in it owned by another colour is dead: 14 squares in all.
The board after step 3 — 0 of 12 queens placed. Step 4. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: rose has one square left, so its queen takes row 12, column 10; indigo has one square left, so its queen takes row 1, column 8; sea green has one square left, so its queen takes row 10, column 9; teal has one square left, so its queen takes row 11, column 1. 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 11, column 1.
Step 5. Mint is down to 4 candidates in rows 3–5, columns 2 and 3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 6. The khaki region has 3 squares left, spread across rows 8 and 9, columns 2 and 3. 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.
The board after step 6 — 4 of 12 queens placed. Step 7. Wherever orange ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Khaki and orange are now boxed into rows 8 and 9 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 8 squares at once.
Step 9. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: pale yellow has one square left, so its queen takes row 7, column 5; slate has one square left, so its queen takes row 5, column 6; column 7 is down to one square, putting a queen on row 3, column 7; mint has one square left, so its queen takes row 4, column 3; row 6 is down to one square, putting a queen on row 6, column 12; orange has one square left, so its queen takes row 9, column 11; khaki has one square left, so its queen takes row 8, column 2; amber has one square left, so its queen takes row 2, column 4. 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 4.
The board after step 9 — 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 #129
Puzzle #129 is one of the easy-rated boards in the 12x12 set. Twelve colors divide its 144 squares, and you win by placing twelve queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
As with every puzzle in this collection, #129 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 #129 are: sea green (2 squares), rose (3 squares), indigo (4 squares), mint (5 squares), teal (5 squares), slate (6 squares), khaki (6 squares), orange (12 squares), amber (15 squares), red (19 squares), pale yellow (29 squares), blue (38 squares). An even split would hand every color 12 squares, so the sea green region is running 10 squares under that average while the blue region is the roomiest area on the grid with 38 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 2 squares, is under far more pressure than blue with 38. A 36-square gap like this one rewards players who start where the choices are fewest.
Square count is only half the story — how a color is arranged counts too. Sea green is the tidiest shape on #129, packing 100% of its 2×1 bounding box, whereas blue straggles across its 8×11 box at just 43%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a easy board.
Sea green: 2 squares across rows 10–11, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.
Rose covers 3 squares, spanning 2 rows and 2 columns (rows 11–12, columns 9–10).
Indigo occupies 4 squares within rows 1–2, columns 8–10.
Mint: 5 squares across rows 3–5, columns 1–3.
Teal covers 5 squares, spanning 3 rows and 3 columns (rows 10–12, columns 1–3).
Slate occupies 6 squares within rows 5–7, columns 5–8.
Khaki: 6 squares across rows 8–11, columns 1–3.
Orange covers 12 squares, spanning 5 rows and 3 columns (rows 8–12, columns 10–12).
Amber occupies 15 squares within rows 1–4, columns 1–6.
Red: 19 squares across rows 1–9, columns 9–12.
Pale yellow covers 29 squares, spanning 6 rows and 6 columns (rows 7–12, columns 3–8).
Blue occupies 38 squares within rows 1–8, columns 1–11.
Where to start on this board
Open on the tightest color. Here that is sea green, confined to 2 squares between rows 10 and 11 and columns 9 and 9. Its queen has nowhere else to go, which means those 2 rows and 1 column carry more constraint than anywhere else on #129.
Because sea green stays inside column 9, its queen belongs to that column and no other region may use it. Cross out the rest of column 9 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
Work outward to the other flat regions next. Indigo 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 #129
A quick way to find the next move is to count how many different colors touch each line. On this board, row 6 is the narrowest, touched by only 3 colors. Column 12 is the tightest column, with 2 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 11, meeting 6 colors, is the opposite case — the busiest line on #129 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.
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 #129 is rated easy
The easy label comes out of four measurable things about #129: one of its regions is locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 3 colors, and its largest and smallest regions differ by 36. Boards that score tight on those measures give up their first queen fast.
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.
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 #129, start hunting for it near column 12.
Here is a shape check that gives nothing away: when #129 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 #129?
Puzzle #129 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #129 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #129, 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 #129?
Start with the sea green region — the most constrained color on this board, with 2 squares spanning rows 10–11 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.