12x12 Queens Puzzle #233
Difficulty: medium. 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 23-step reasoning is written out below.
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Step-by-step solution for puzzle #233
What follows is a complete solve of puzzle #233, worked the way a person works it rather than the way a computer does. It runs to 23 deductions — 12 queen placements and 11 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 proof by contradiction.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows, proof by contradiction, line confined to one region, pairing argument on columns.
Show the full walkthrough (16 steps) — contains the solution
Step 1. Only row 2, column 1 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 1, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. The orange region is down to one open square, at row 9, column 12. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 12, the remaining orange squares, and the ring of neighbours around row 9, column 12.
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: 7 squares in all.
Step 4. The blue region is down to one open square, at row 3, column 11. Every colour holds exactly one queen, so that square is forced. Row 3 and column 11 are now spoken for, along with the squares touching that queen.
Step 5. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 7 squares in all.
The board after step 5 — 3 of 12 queens placed. Step 6. The red region has 4 squares left, spread across rows 5–7, columns 9 and 10. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 7. Wherever sea green ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Here is the pairing argument. The khaki, sea green, teal, and rose regions have no open squares outside rows 8, 10, 11, and 12 — 4 colours confined to 4 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 9. Test row 1, column 7 for indigo: place a queen there, run the forced consequences through, and the rose region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 10. The indigo region is down to one open square, at row 1, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 6, the remaining indigo squares, and the ring of neighbours around row 1, column 6.
Step 11. Sea green is down to 4 candidates in rows 10 and 11, columns 5, 7, and 8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about sea green itself.
The board after step 11 — 4 of 12 queens placed. Step 12. The khaki region has 3 squares left, spread across rows 8 and 10, columns 9 and 10. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 13. Row 8 has only khaki squares left (2 open squares). The row needs a queen and only khaki can provide one, which pins that colour to this row and kills its squares elsewhere: 1 square.
Step 14. All of the khaki region's remaining squares (2 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 15. Red and khaki are now boxed into columns 9 and 10 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 6 squares at once.
Step 16. 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: mint has one square left, so its queen takes row 4, column 7; rose has one square left, so its queen takes row 12, column 8; sea green has one square left, so its queen takes row 10, column 5; pale yellow has one square left, so its queen takes row 7, column 4; teal has one square left, so its queen takes row 11, column 2; slate has one square left, so its queen takes row 5, column 3; red has one square left, so its queen takes row 6, column 10; khaki has one square left, so its queen takes row 8, 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 8, column 9.
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 #233
Puzzle #233 is one of the medium-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.
There is exactly one way to finish #233, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these twelve regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #233 are: amber (1 square), orange (1 square), indigo (7 squares), mint (9 squares), red (9 squares), sea green (9 squares), blue (13 squares), teal (13 squares), rose (13 squares), khaki (14 squares), pale yellow (25 squares), slate (30 squares). An even split would hand every color 12 squares, so the amber region is running 11 squares under that average while the slate region is the roomiest area on the grid with 30 squares.
Every color takes one queen and one only, whatever its size — which is why the 29 square difference between amber and slate 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. Amber is the tidiest shape on #233, packing 100% of its 1×1 bounding box, whereas pale yellow straggles across its 8×8 box at just 39%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #233 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.
Amber occupies 1 square within rows 2–2, columns 1–1. It never leaves row 2, so its queen is locked to that row.
Orange: 1 square across rows 9–9, columns 12–12. It never leaves row 9, so its queen is locked to that row.
Indigo covers 7 squares, spanning 2 rows and 5 columns (rows 1–2, columns 4–8).
Mint occupies 9 squares within rows 3–4, columns 4–10.
Red: 9 squares across rows 4–7, columns 9–12.
Sea green covers 9 squares, spanning 4 rows and 4 columns (rows 8–11, columns 5–8).
Blue occupies 13 squares within rows 1–5, columns 8–12.
Teal: 13 squares across rows 9–12, columns 1–5.
Rose covers 13 squares, spanning 3 rows and 7 columns (rows 10–12, columns 6–12).
Khaki occupies 14 squares within rows 7–10, columns 8–12.
Pale yellow: 25 squares across rows 4–11, columns 2–9.
Slate covers 30 squares, spanning 8 rows and 6 columns (rows 1–8, columns 1–6).
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 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #233.
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. Orange, indigo and mint 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 #233
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. Columns 1, 2 and 3 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 11 rows. Row 10, meeting 5 colors, is the opposite case — the busiest line on #233 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.
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 #233 is rated medium
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 2 colors, and a region-size spread of 29. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a medium board from the rest.
Stuck on #233 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 #233 is row 12.
Here is a shape check that gives nothing away: when #233 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 #233?
Puzzle #233 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #233 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #233, 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 #233?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.