12x12 Queens Puzzle #33
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 25-step reasoning is written out below.
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Step-by-step solution for puzzle #33
What follows is a complete solve of puzzle #33, worked the way a person works it rather than the way a computer does. It runs to 25 deductions — 12 queen placements and 13 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 rows, pairing argument on columns, last square in a row, last square in a column.
Show the full walkthrough (16 steps) — contains the solution
Step 1. Only row 10, column 12 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 12, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (3 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 9 squares come off.
Step 3. The blue region has 3 squares left, spread across rows 2 and 3, columns 8 and 9. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
Step 4. All of the mint region's remaining squares (3 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 5. Slate is down to 6 candidates in rows 5–7, columns 6–8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
The board after step 5 — 1 of 12 queens placed. Step 6. All of the orange region's remaining squares (3 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 7. Red cannot leave column 2 — every one of its open squares (3 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 8 squares in all.
Step 8. Teal is down to 4 candidates in rows 11 and 12, columns 8–10, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about teal itself.
Step 9. Teal and rose are now boxed into rows 11 and 12 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 6 squares at once.
Step 10. The orange region is down to one open square, at row 9, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 1, the remaining orange squares, and the ring of neighbours around row 9, column 1.
Step 11. Red cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 1 square in all.
The board after step 11 — 2 of 12 queens placed. Step 12. The khaki region has 3 squares left, spread across rows 7 and 8, columns 3 and 6. 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 13. Blue, pale yellow, and teal are now boxed into columns 8–10 and nothing else. That is 3 colours needing 3 columns, so they fill those columns between them — which locks every remaining colour out and removes 3 squares at once.
Step 14. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 15. Indigo and slate are now boxed into columns 6 and 7 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 9 squares at once.
Step 16. 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: khaki has one square left, so its queen takes row 8, column 3; red has one square left, so its queen takes row 6, column 2; row 11 is down to one square, putting a queen on row 11, column 8; blue has one square left, so its queen takes row 3, column 9; column 6 is down to one square, putting a queen on row 1, column 6; row 2 is down to one square, putting a queen on row 2, column 4; rose has one square left, so its queen takes row 12, column 5; row 4 is down to one square, putting a queen on row 4, column 11; pale yellow has one square left, so its queen takes row 7, column 10; slate has one square left, so its queen takes row 5, column 7. 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 7.
The board after step 16 — 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 #33
Puzzle #33 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.
Like every board on this site, #33 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #33 are: sea green (1 square), indigo (3 squares), blue (4 squares), orange (4 squares), slate (7 squares), red (7 squares), rose (8 squares), mint (10 squares), teal (13 squares), khaki (18 squares), pale yellow (30 squares), amber (39 squares). An even split would hand every color 12 squares, so the sea green region is running 11 squares under that average while the amber region is the roomiest area on the grid with 39 squares.
Every color takes one queen and one only, whatever its size — which is why the 38 square difference between sea green and amber 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 #33, packing 100% of its 1×3 bounding box, whereas teal straggles across its 6×5 box at just 43%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #33 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Sea green: 1 square across rows 10–10, columns 12–12. It never leaves row 10, so its queen is locked to that row.
Indigo covers 3 squares, spanning 1 row and 3 columns (rows 1–1, columns 6–8). It never leaves row 1, so its queen is locked to that row.
Blue occupies 4 squares within rows 2–3, columns 7–9.
Orange: 4 squares across rows 9–12, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Slate covers 7 squares, spanning 4 rows and 3 columns (rows 4–7, columns 6–8).
Red occupies 7 squares within rows 5–8, columns 1–2.
Rose: 8 squares across rows 11–12, columns 2–7.
Mint covers 10 squares, spanning 5 rows and 4 columns (rows 1–5, columns 9–12).
Teal occupies 13 squares within rows 7–12, columns 8–12.
Khaki: 18 squares across rows 6–11, columns 2–7.
Pale yellow covers 30 squares, spanning 10 rows and 6 columns (rows 2–11, columns 7–12).
Amber occupies 39 squares within rows 1–10, columns 1–7.
Where to start on this board
Open on the tightest color. Here that is sea green, confined to 1 square between rows 10 and 10 and columns 12 and 12. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #33.
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. Indigo, blue 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 #33
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 1, 3, 4, 5, 10 and 11 are the tightest columns, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 11 rows. Row 10 sits at the far end with 6 colors crossing it; it will almost certainly be among the last to settle.
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.
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 #33 is rated easy
What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 38. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
If #33 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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 #33 is row 1.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 8 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #33?
Puzzle #33 is rated easy. 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 #33 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #33, 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 #33?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 12–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.