12x12 Queens Puzzle #133
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #133
What follows is a complete solve of puzzle #133, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 12 queen placements and 4 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 columns.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on columns.
Show the full walkthrough (7 steps) — contains the solution
Step 1. Only row 2, column 6 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 6, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. The teal region is down to one open square, at row 11, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 10, the remaining teal squares, and the ring of neighbours around row 11, column 10.
Step 3. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 6 squares in all.
Step 4. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.
The board after step 4 — 2 of 12 queens placed. Step 5. Mint is down to 3 candidates in rows 4 and 5, columns 1–3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 6. Here is the pairing argument. The indigo and blue regions have no open squares outside columns 2 and 3 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 14 squares come off in one stroke.
Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 10 queens fall out in order without any new idea being needed: mint has one square left, so its queen takes row 4, column 1; blue has one square left, so its queen takes row 3, column 3; indigo has one square left, so its queen takes row 1, column 2; khaki has one square left, so its queen takes row 8, column 4; slate has one square left, so its queen takes row 5, column 5; sea green has one square left, so its queen takes row 10, column 7; rose has one square left, so its queen takes row 12, column 8; red has one square left, so its queen takes row 6, column 9; orange has one square left, so its queen takes row 9, column 11; pale yellow has one square left, so its queen takes row 7, 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 7, column 12.
The board after step 7 — 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 #133
Puzzle #133 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, #133 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 #133 are: amber (1 square), teal (1 square), indigo (2 squares), khaki (5 squares), mint (6 squares), rose (10 squares), blue (14 squares), pale yellow (14 squares), slate (20 squares), sea green (20 squares), orange (23 squares), red (28 squares). An even split would hand every color 12 squares, so the amber region is running 11 squares under that average while the red region is the roomiest area on the grid with 28 squares.
Every color takes one queen and one only, whatever its size — which is why the 27 square difference between amber and red is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #133, packing 100% of its 1×2 bounding box, whereas orange straggles across its 7×8 box at just 41%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #133, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Amber covers 1 square, spanning 1 row and 1 column (rows 2–2, columns 6–6). It never leaves row 2, so its queen is locked to that row.
Teal occupies 1 square within rows 11–11, columns 10–10. It never leaves row 11, so its queen is locked to that row.
Indigo: 2 squares across rows 1–1, columns 2–3. It never leaves row 1, so its queen is locked to that row.
Khaki covers 5 squares, spanning 2 rows and 3 columns (rows 8–9, columns 2–4).
Mint occupies 6 squares within rows 3–5, columns 1–3.
Rose: 10 squares across rows 10–12, columns 6–10.
Blue covers 14 squares, spanning 3 rows and 7 columns (rows 1–3, columns 1–7).
Pale yellow occupies 14 squares within rows 2–9, columns 11–12.
Slate: 20 squares across rows 3–10, columns 1–6.
Sea green covers 20 squares, spanning 4 rows and 7 columns (rows 9–12, columns 1–7).
Orange occupies 23 squares within rows 6–12, columns 5–12.
Red: 28 squares across rows 1–7, columns 6–12.
Where to start on this board
Open on the tightest color. Here that is amber, confined to 1 square between rows 2 and 2 and columns 6 and 6. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #133.
Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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. Indigo, teal and khaki 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 #133
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 12 are the narrowest, touched by only 3 colors. Columns 8, 9, 11 and 12 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 11 rows. Row 9 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
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.
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 #133 is rated easy
The rating reflects how much the board concedes up front. Puzzle #133 has five 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 27 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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #133 is row 1.
A non-spoiling distribution check: solved, #133 carries 4 queens on the perimeter against 8 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
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 #133?
Puzzle #133 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #133 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #133, 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 #133?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.