12x12 Queens Puzzle #119
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 25-step reasoning is written out below.
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Step-by-step solution for puzzle #119
What follows is a complete solve of puzzle #119, 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 proof by contradiction.
Techniques this board needs: last square in a region, region shadow, pairing argument on columns, proof by contradiction, last square in a column.
Show the full walkthrough (17 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: sea green has one square left, so its queen takes row 10, column 8; indigo has one square left, so its queen takes row 1, column 9; rose has one square left, so its queen takes row 12, column 12; amber has one square left, so its queen takes row 2, column 11; blue has one square left, so its queen takes row 3, column 6; teal has one square left, so its queen takes row 11, column 1. 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 11, column 1.
Step 2. Wherever mint ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 3. Slate is down to 4 candidates in rows 4, 5, 7, and 8, columns 7 and 10, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
Step 4. The khaki region has 3 squares left, spread across rows 8 and 9, columns 2 and 5. 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.
The board after step 4 — 6 of 12 queens placed. Step 5. Wherever pale yellow ends up among its 7 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 6. Orange is down to 3 candidates in rows 6, 8, and 9, columns 7 and 10, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about orange itself.
Step 7. Here is the pairing argument. The slate and orange regions have no open squares outside columns 7 and 10 — 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: 2 squares come off in one stroke.
Step 8. Test row 5, column 4 for mint: place a queen there, run the forced consequences through, and column 3 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 9. Now a short proof by contradiction. Suppose the mint queen went to row 5, column 5. Follow the forced moves that would create and column 4 runs out of open squares entirely — impossible. So that square is ruled out for good.
The board after step 9 — 6 of 12 queens placed. Step 10. Test row 6, column 5 for mint: place a queen there, run the forced consequences through, and the khaki region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 11. The mint region is down to one open square, at row 4, column 4. Every colour holds exactly one queen, so that square is forced. Row 4 and column 4 are now spoken for, along with the squares touching that queen.
Step 12. Test row 7, column 10 for slate: place a queen there, run the forced consequences through, and the pale yellow region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 13. The slate region is down to one open square, at row 5, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 7, the remaining slate squares, and the ring of neighbours around row 5, column 7.
The board after step 13 — 8 of 12 queens placed. Step 14. Wherever red ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 15. Now a short proof by contradiction. Suppose the red queen went to row 6, column 2. Follow the forced moves that would create and the orange region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 16. The red region has 2 squares left, spread across rows 6 and 7, columns 2 and 3. 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 17. 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: column 3 is down to one square, putting a queen on row 6, column 3; orange has one square left, so its queen takes row 9, column 10; khaki has one square left, so its queen takes row 8, column 2; pale yellow has one square left, so its queen takes row 7, column 5. 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 5.
The board after step 17 — 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 #119
12x12 puzzle #119 is rated hard. Twelve colored regions cover its 144 squares, and your job is to seat twelve queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Puzzle #119 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 #119 are: sea green (1 square), rose (1 square), indigo (2 squares), teal (5 squares), blue (7 squares), amber (8 squares), mint (11 squares), pale yellow (12 squares), khaki (16 squares), slate (20 squares), red (21 squares), orange (40 squares). An even split would hand every color 12 squares, so the sea green region is running 11 squares under that average while the orange region is the roomiest area on the grid with 40 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Sea green has only 1 place to put its queen; orange has 40. The spread between them on this board is 39 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×2 box that encloses it, while khaki is the most scattered at 53% of its 6×5 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
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.
Sea green occupies 1 square within rows 10–10, columns 8–8. It never leaves row 10, so its queen is locked to that row.
Rose: 1 square across rows 12–12, columns 12–12. It never leaves row 12, so its queen is locked to that row.
Indigo covers 2 squares, spanning 1 row and 2 columns (rows 1–1, columns 8–9). It never leaves row 1, so its queen is locked to that row.
Teal occupies 5 squares within rows 10–12, columns 1–3.
Blue: 7 squares across rows 1–3, columns 4–7.
Amber covers 8 squares, spanning 2 rows and 5 columns (rows 1–2, columns 8–12).
Mint occupies 11 squares within rows 2–6, columns 4–7.
Pale yellow: 12 squares across rows 7–10, columns 3–7.
Khaki covers 16 squares, spanning 6 rows and 5 columns (rows 7–12, columns 1–5).
Slate occupies 20 squares within rows 3–8, columns 6–11.
Red: 21 squares across rows 1–7, columns 1–4.
Orange covers 40 squares, spanning 10 rows and 7 columns (rows 3–12, columns 6–12).
Where to start on this board
Begin where the choices are fewest. On this board that means sea green, which owns just 1 square inside a 1×1 window running from row 10 to row 10 and column 8 to column 8. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
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, rose and amber 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 #119
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 9 and 11 are the narrowest, touched by only 3 colors. Columns 1, 2, 10, 11 and 12 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 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 #119 and the last one you should expect to crack.
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 #119 is rated hard
The hard label comes out of four measurable things about #119: five of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 39. Boards that score tight on those measures give up their first queen fast.
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.
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 #119 the place to look for one is around row 9.
Here is a shape check that gives nothing away: when #119 is solved, 3 queens sit on the outer edge of the grid and 9 sit inside it, with 1 queen 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 #119?
Puzzle #119 is rated hard. 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 #119 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #119, 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 #119?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.