12x12 Queens Puzzle #258
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #258
What follows is a complete solve of puzzle #258, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 12 queen placements and 6 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, last square in a column.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Only row 4, column 3 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 3, the rest of the mint 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. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 9 squares in all.
Step 4. The blue region is down to one open square, at row 3, column 12. Every colour holds exactly one queen, so that square is forced. Row 3 and column 12 are now spoken for, along with the squares touching that queen.
Step 5. Pale yellow is down to 4 candidates in rows 6 and 7, columns 4–6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about pale yellow itself.
The board after step 5 — 2 of 12 queens placed. Step 6. Here is the pairing argument. The amber and khaki regions have no open squares outside columns 1 and 2 — 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: 9 squares come off in one stroke.
Step 7. Only row 6, column 4 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 4, in red and in the ring around that square is now dead.
Step 8. The pale yellow region is down to one open square, at row 7, column 6. Every colour holds exactly one queen, so that square is forced. Row 7 and column 6 are now spoken for, along with the squares touching that queen.
Step 9. Scan column 2 and only row 2, column 2 remains — a amber square. Every column takes a queen, so it takes this one. Row 2 and column 2 are now spoken for, along with the squares touching that queen.
Step 10. 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: 4 squares come off.
The board after step 10 — 5 of 12 queens placed. Step 11. 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: khaki has one square left, so its queen takes row 8, column 1; orange has one square left, so its queen takes row 9, column 7; slate has one square left, so its queen takes row 5, column 8; indigo has one square left, so its queen takes row 1, 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 1, column 9.
Step 12. Sea green cannot leave column 10 — 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: 3 squares in all.
Step 13. The rose region is down to one open square, at row 12, column 11. Every colour holds exactly one queen, so that square is forced. Row 12 and column 11 are now spoken for, along with the squares touching that queen.
Step 14. Only row 10, column 10 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 10, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 15. The teal region is down to one open square, at row 11, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 5, the remaining teal squares, and the ring of neighbours around row 11, column 5.
The board after step 15 — 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 #258
Board #258 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 #258 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 #258 are: mint (1 square), indigo (3 squares), pale yellow (4 squares), blue (6 squares), rose (8 squares), amber (9 squares), khaki (9 squares), red (13 squares), sea green (13 squares), orange (16 squares), teal (21 squares), slate (41 squares). An even split would hand every color 12 squares, so the mint region is running 11 squares under that average while the slate region is the roomiest area on the grid with 41 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 mint, with 1 square, is under far more pressure than slate with 41. A 40-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×3 frame; orange is the loosest, occupying only 38% of its 7×6 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Below is every color on #258 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.
Mint: 1 square across rows 4–4, columns 3–3. It never leaves row 4, so its queen is locked to that row.
Indigo covers 3 squares, spanning 1 row and 3 columns (rows 1–1, columns 7–9). It never leaves row 1, so its queen is locked to that row.
Pale yellow occupies 4 squares within rows 6–7, columns 4–6.
Blue: 6 squares across rows 1–3, columns 10–12.
Rose covers 8 squares, spanning 4 rows and 3 columns (rows 9–12, columns 10–12).
Amber occupies 9 squares within rows 1–3, columns 1–4.
Khaki: 9 squares across rows 3–8, columns 1–2.
Red covers 13 squares, spanning 6 rows and 5 columns (rows 5–10, columns 1–5).
Sea green occupies 13 squares within rows 8–12, columns 8–11.
Orange: 16 squares across rows 5–11, columns 6–11.
Teal covers 21 squares, spanning 5 rows and 7 columns (rows 8–12, columns 1–7).
Slate occupies 41 squares within rows 1–9, columns 4–12.
Where to start on this board
Mint is the natural opening on #258: it is the smallest region on the grid at 1 square, boxed into rows 4–4 and columns 3–3. 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 mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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 pale yellow 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 #258
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 4 and 12 are the narrowest, touched by only 3 colors. Column 12 is the tightest column, 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 6 colors — worth revisiting later, not now.
Working through the middle game
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
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.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #258 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 40. 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 hard board from the rest.
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.
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 #258, start hunting for it near row 2.
A non-spoiling distribution check: solved, #258 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 #258?
Puzzle #258 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #258 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #258, 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 #258?
Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.