12x12 Queens Puzzle #43
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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #43
What follows is a complete solve of puzzle #43, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 12 queen placements and 5 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 rows.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 12, column 7 is still open in rose, and since each colour must take a queen, that settles it. That clears row 12, column 7, 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 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 4, the remaining teal squares, and the ring of neighbours around row 11, column 4.
Step 3. Red cannot leave column 1 — every one of its open squares (3 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 8 squares in all.
Step 4. The sea green region is down to one open square, at row 10, column 2. Every colour holds exactly one queen, so that square is forced. Row 10 and column 2 are now spoken for, along with the squares touching that queen.
The board after step 4 — 3 of 12 queens placed. Step 5. Only row 9, column 6 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 6, the rest of the orange region and every square adjacent to it — diagonals included.
Step 6. The khaki region has 4 squares left, spread across rows 7 and 8, columns 5, 8, and 9. 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 slate 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.
The board after step 7 — 4 of 12 queens placed. Step 8. Here is the pairing argument. The pale yellow and khaki regions have no open squares outside rows 7 and 8 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 4 squares come off in one stroke.
Step 9. 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: red has one square left, so its queen takes row 6, column 1; slate has one square left, so its queen takes row 5, column 11; mint has one square left, so its queen takes row 4, column 3; blue has one square left, so its queen takes row 3, 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 3, column 10.
Step 10. Pale yellow cannot leave column 12 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 2 squares in all.
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: indigo has one square left, so its queen takes row 1, column 9; amber has one square left, so its queen takes row 2, column 5; khaki has one square left, so its queen takes row 8, column 8; pale yellow has one square left, so its queen takes row 7, column 12. 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 12.
The board after step 11 — 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 #43
12x12 puzzle #43 is rated easy. 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.
There is exactly one way to finish #43, 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 #43 are: rose (1 square), teal (2 squares), red (3 squares), slate (6 squares), indigo (8 squares), sea green (10 squares), khaki (12 squares), blue (13 squares), pale yellow (15 squares), orange (23 squares), mint (25 squares), amber (26 squares). An even split would hand every color 12 squares, so the rose region is running 11 squares under that average while the amber region is the roomiest area on the grid with 26 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; amber has 26. The spread between them on this board is 25 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here red is the most solid, filling 100% of its 3×1 box, and slate the most diffuse at 50% of its 3×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Rose covers 1 square, spanning 1 row and 1 column (rows 12–12, columns 7–7). It never leaves row 12, so its queen is locked to that row.
Teal occupies 2 squares within rows 11–12, columns 4–4. It sits wholly inside column 4, so its queen must be in that column.
Red: 3 squares across rows 6–8, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Slate covers 6 squares, spanning 3 rows and 4 columns (rows 5–7, columns 8–11).
Indigo occupies 8 squares within rows 1–3, columns 9–12.
Sea green: 10 squares across rows 9–12, columns 1–3.
Khaki covers 12 squares, spanning 4 rows and 5 columns (rows 6–9, columns 5–9).
Blue occupies 13 squares within rows 3–5, columns 7–12.
Pale yellow: 15 squares across rows 6–11, columns 10–12.
Orange covers 23 squares, spanning 5 rows and 9 columns (rows 8–12, columns 4–12).
Mint occupies 25 squares within rows 3–9, columns 1–7.
Amber: 26 squares across rows 1–4, columns 1–9.
Where to start on this board
Begin where the choices are fewest. On this board that means rose, which owns just 1 square inside a 1×1 window running from row 12 to row 12 and column 7 to column 7. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
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. Teal is no more than two rows tall, so its queen is 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 #43
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 2 are the narrowest, touched by only 2 colors. Columns 2 and 3 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 2 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 5 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.
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.
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 #43 is rated easy
Ratings track how generous the opening is. On #43 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 25-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
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.
Stuck on #43 despite the easy 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.
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 #43 the place to look for one is around row 1.
A non-spoiling distribution check: solved, #43 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 #43?
Puzzle #43 is rated easy. 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 #43 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #43, 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 #43?
Start with the rose region — the most constrained color on this board, with 1 square spanning rows 12–12 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.