12x12 Queens Puzzle #144
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 21-step reasoning is written out below.
Previous puzzle · All 12x12 puzzles · Next puzzle
Step-by-step solution for puzzle #144
What follows is a complete solve of puzzle #144, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 12 queen placements and 9 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, pairing argument on columns, proof by contradiction.
Show the full walkthrough (13 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: indigo has one square left, so its queen takes row 1, column 12; red has one square left, so its queen takes row 6, column 11; amber has one square left, so its queen takes row 2, column 9; rose has one square left, so its queen takes row 12, column 2; sea green has one square left, so its queen takes row 10, column 1; pale yellow has one square left, so its queen takes row 7, column 3. 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 3.
Step 2. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 4 squares in all.
Step 3. Slate is down to 2 candidates in rows 4 and 5, columns 8 and 10, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about slate itself.
Step 4. The orange region has 2 squares left, spread across rows 9 and 11, columns 4 and 5. 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.
The board after step 4 — 6 of 12 queens placed. Step 5. Here is the pairing argument. The khaki, orange, and teal regions have no open squares outside rows 8, 9, and 11 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 2 squares come off in one stroke.
Step 6. Blue and orange are now boxed into columns 4 and 5 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 2 squares at once.
Step 7. Now a short proof by contradiction. Suppose the blue queen went to row 3, column 5. Follow the forced moves that would create and the teal region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 8. Only row 3, column 4 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 4, the rest of the blue region and every square adjacent to it — diagonals included.
Step 9. The orange region is down to one open square, at row 9, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 5, the remaining orange squares, and the ring of neighbours around row 9, column 5.
The board after step 9 — 8 of 12 queens placed. Step 10. The teal region has 3 squares left, spread across rows 8 and 11, columns 6–8. 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 11. Now a short proof by contradiction. Suppose the mint queen went to row 5, column 6. Follow the forced moves that would create and the teal region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 12. Test row 5, column 7 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 13. 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: 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; teal has one square left, so its queen takes row 11, column 7; khaki has one square left, so its queen takes row 8, column 10. 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 10.
The board after step 13 — 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 #144
This is puzzle number 144 in the 12x12 collection, rated easy. The grid holds 144 squares split between twelve colored regions, and a finished board carries twelve queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
Puzzle #144 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 #144 are: indigo (1 square), rose (1 square), red (2 squares), sea green (5 squares), amber (8 squares), orange (9 squares), slate (14 squares), pale yellow (15 squares), teal (16 squares), blue (18 squares), mint (26 squares), khaki (29 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the khaki region is the roomiest area on the grid with 29 squares.
Every color takes one queen and one only, whatever its size — which is why the 28 square difference between indigo and khaki 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 #144, packing 100% of its 1×1 bounding box, whereas mint straggles across its 9×6 box at just 48%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #144 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.
Indigo: 1 square across rows 1–1, columns 12–12. It never leaves row 1, so its queen is locked to that row.
Rose covers 1 square, spanning 1 row and 1 column (rows 12–12, columns 2–2). It never leaves row 12, so its queen is locked to that row.
Red occupies 2 squares within rows 6–6, columns 11–12. It never leaves row 6, so its queen is locked to that row.
Sea green: 5 squares across rows 10–12, columns 1–3.
Amber covers 8 squares, spanning 3 rows and 4 columns (rows 1–3, columns 9–12).
Orange occupies 9 squares within rows 9–12, columns 2–5.
Slate: 14 squares across rows 2–6, columns 8–12.
Pale yellow covers 15 squares, spanning 6 rows and 5 columns (rows 4–9, columns 1–5).
Teal occupies 16 squares within rows 8–12, columns 5–9.
Blue: 18 squares across rows 1–5, columns 1–5.
Mint covers 26 squares, spanning 9 rows and 6 columns (rows 1–9, columns 3–8).
Khaki occupies 29 squares within rows 6–12, columns 7–12.
Where to start on this board
The most constrained color is where a solve should begin, and on #144 that is indigo with 1 square. It reaches from row 1 to row 1 and from column 12 to column 12 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Red 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 #144
A quick way to find the next move is to count how many different colors touch each line. On this board, row 7 is the narrowest, touched by only 3 colors. Column 6 is the tightest column, with 2 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 12, meeting 5 colors, is the opposite case — the busiest line on #144 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.
With twelve queens to seat and twelve regions competing over 144 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 12x12 boards quickly and players who stall halfway.
Resist the plausible-looking queen. On #144 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 #144 is rated easy
What earns a board its rating is the shape of its opening. Here that opening offers five single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 28. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
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 #144 is column 6.
Here is a shape check that gives nothing away: when #144 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 12x12 Queens puzzle #144?
Puzzle #144 is rated easy. 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 #144 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #144, 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 #144?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 12–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.