12x12 Queens Puzzle #234
Difficulty: hard. 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 #234
What follows is a complete solve of puzzle #234, 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 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.
Show the full walkthrough (19 steps) — contains the solution
Step 1. Only row 12, column 4 is still open in rose, and since each colour must take a queen, that settles it. That clears row 12, column 4, the rest of the rose region and every square adjacent to it — diagonals included.
Step 2. The teal region is down to one open square, at row 11, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 1, the remaining teal squares, and the ring of neighbours around row 11, column 1.
Step 3. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 8 squares in all.
Step 4. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 9 squares come off.
Step 5. Red is down to 4 candidates in rows 4–6, columns 2 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about red itself.
The board after step 5 — 2 of 12 queens placed. Step 6. All of the orange region's remaining squares (2 open squares) lie in column 12. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 8 squares come off.
Step 7. Blue cannot leave column 11 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 6 squares in all.
Step 8. The sea green region is down to one open square, at row 10, column 10. Every colour holds exactly one queen, so that square is forced. Row 10 and column 10 are now spoken for, along with the squares touching that queen.
Step 9. Only row 1, column 9 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 9, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 10. 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.
The board after step 10 — 5 of 12 queens placed. Step 11. Slate is down to 3 candidates in rows 5 and 6, columns 7 and 8, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about slate itself.
Step 12. Here is the pairing argument. The blue, mint, slate, and red regions have no open squares outside rows 3–6 — 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: 1 square come off in one stroke.
Step 13. Amber and red are now boxed into columns 2 and 3 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 4 squares at once.
Step 14. The khaki region is down to one open square, at row 8, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 5, the remaining khaki squares, and the ring of neighbours around row 8, column 5.
The board after step 14 — 6 of 12 queens placed. Step 15. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 1 square in all.
Step 16. Row 6 has a single open square left, at column 3 in the red region. Every row needs a queen, so this one is forced. Cross out the whole of row 6 and column 3, the remaining red squares, and the ring of neighbours around row 6, column 3.
Step 17. Only row 2, column 2 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 2, the rest of the amber region and every square adjacent to it — diagonals included.
Step 18. All of the slate region's remaining squares (2 open squares) lie in row 5. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
Step 19. 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: blue has one square left, so its queen takes row 3, column 11; mint has one square left, so its queen takes row 4, column 6; slate has one square left, so its queen takes row 5, column 8; pale yellow has one square left, so its queen takes row 7, 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 7, column 7.
The board after step 19 — 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 #234
Board #234 of the 12x12 bank carries a hard 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.
Puzzle #234 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #234 are: rose (1 square), indigo (3 squares), orange (4 squares), teal (6 squares), amber (7 squares), red (7 squares), blue (12 squares), slate (14 squares), sea green (17 squares), khaki (22 squares), pale yellow (24 squares), mint (27 squares). An even split would hand every color 12 squares, so the rose region is running 11 squares under that average while the mint region is the roomiest area on the grid with 27 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Rose has only 1 place to put its queen; mint has 27. The spread between them on this board is 26 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×3 frame; sea green is the loosest, occupying only 40% of its 6×7 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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 hard board.
Rose: 1 square across rows 12–12, columns 4–4. It never leaves row 12, so its queen is locked to that row.
Indigo covers 3 squares, spanning 1 row and 3 columns (rows 1–1, columns 9–11). It never leaves row 1, so its queen is locked to that row.
Orange occupies 4 squares within rows 9–12, columns 12–12. It sits wholly inside column 12, so its queen must be in that column.
Teal: 6 squares across rows 11–12, columns 1–4.
Amber covers 7 squares, spanning 3 rows and 3 columns (rows 1–3, columns 1–3).
Red occupies 7 squares within rows 3–6, columns 1–3.
Blue: 12 squares across rows 1–8, columns 10–12.
Slate covers 14 squares, spanning 5 rows and 5 columns (rows 2–6, columns 7–11).
Sea green occupies 17 squares within rows 7–12, columns 5–11.
Khaki: 22 squares across rows 6–11, columns 1–5.
Pale yellow covers 24 squares, spanning 6 rows and 6 columns (rows 6–11, columns 5–10).
Mint occupies 27 squares within rows 1–6, columns 3–8.
Where to start on this board
Rose is the natural opening on #234: it is the smallest region on the grid at 1 square, boxed into rows 12–12 and columns 4–4. 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 rose never leaves row 12, its queen must be in that row — and that instantly settles row 12 for everyone else. Sweep along it and X out every square that is not rose. 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 and teal 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 #234
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 4, 5, 7, 8, 9, 10 and 12 are the narrowest, touched by only 4 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 4 colors has to be claimed by one of them, which pushes every remaining region into the other 11 rows. Row 6, meeting 6 colors, is the opposite case — the busiest line on #234 and the last one you should expect to crack.
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.
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.
Resist the plausible-looking queen. On #234 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #234 is rated hard
The hard label comes out of four measurable things about #234: four of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 4 colors, and its largest and smallest regions differ by 26. Boards that score tight on those measures give up their first queen fast.
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.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #234 the place to look for one is around column 12.
Here is a shape check that gives nothing away: when #234 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 #234?
Puzzle #234 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 4 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #234 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #234, 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 #234?
Start with the rose region — the most constrained color on this board, with 1 square spanning rows 12–12 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.