12x12 Queens Puzzle #293
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 23-step reasoning is written out below.
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Step-by-step solution for puzzle #293
What follows is a complete solve of puzzle #293, worked the way a person works it rather than the way a computer does. It runs to 23 deductions — 12 queen placements and 11 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: region confined to one line, region shadow, pairing argument on rows, last square in a region, pairing argument on columns, last square in a column.
Show the full walkthrough (17 steps) — contains the solution
Step 1. Slate cannot leave row 5 — every one of its open squares (2 open squares) sits there. That row belongs to slate, so every square on it owned by another colour is dead: 14 squares in all.
Step 2. All of the pale yellow region's remaining squares (6 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 3. Blue cannot leave column 2 — every one of its open squares (4 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 7 squares in all.
Step 4. Wherever teal ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
The board after step 4 — 0 of 12 queens placed. Step 5. Rose is down to 5 candidates in rows 10–12, columns 9–11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about rose itself.
Step 6. Here is the pairing argument. The sea green, teal, and rose regions have no open squares outside rows 10–12 — 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: 12 squares come off in one stroke.
Step 7. Pale yellow cannot leave column 1 — every one of its open squares (3 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 1 square in all.
Step 8. All of the orange region's remaining squares (2 open squares) lie in column 10. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 10 squares come off.
Step 9. Only row 5, column 9 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 9, the rest of the slate region and every square adjacent to it — diagonals included.
The board after step 9 — 1 of 12 queens placed. Step 10. 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. Cross out the whole of row 12 and column 11, the remaining rose squares, and the ring of neighbours around row 12, column 11.
Step 11. Amber and khaki are now boxed into columns 8 and 12 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 5 squares at once.
Step 12. The teal region is down to one open square, at row 11, column 7. Every colour holds exactly one queen, so that square is forced. Row 11 and column 7 are now spoken for, along with the squares touching that queen.
Step 13. Only row 10, column 5 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 5, the rest of the sea green region and every square adjacent to it — diagonals included.
The board after step 13 — 4 of 12 queens placed. Step 14. Here is the pairing argument. The red, pale yellow, khaki, and orange regions have no open squares outside rows 6–9 — 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: 4 squares come off in one stroke.
Step 15. Only row 3, column 2 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 2, in blue and in the ring around that square is now dead.
Step 16. 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: 2 squares come off.
Step 17. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: column 8 is down to one square, putting a queen on row 8, column 8; orange has one square left, so its queen takes row 9, column 10; pale yellow has one square left, so its queen takes row 7, column 1; red has one square left, so its queen takes row 6, column 6; column 3 is down to one square, putting a queen on row 1, column 3; mint has one square left, so its queen takes row 4, column 4; amber has one square left, so its queen takes row 2, 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 2, column 12.
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 #293
Puzzle #293 is one of the easy-rated boards in the 12x12 set. Twelve colors divide its 144 squares, and you win by placing twelve queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
As with every puzzle in this collection, #293 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #293 are: slate (2 squares), teal (4 squares), pale yellow (6 squares), rose (6 squares), blue (9 squares), orange (9 squares), indigo (10 squares), sea green (13 squares), amber (15 squares), khaki (16 squares), mint (22 squares), red (32 squares). An even split would hand every color 12 squares, so the slate region is running 10 squares under that average while the red region is the roomiest area on the grid with 32 squares.
Every color takes one queen and one only, whatever its size — which is why the 30 square difference between slate and red 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. Slate is the tidiest shape on #293, packing 100% of its 1×2 bounding box, whereas mint straggles across its 6×10 box at just 37%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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 easy board.
Slate occupies 2 squares within rows 5–5, columns 9–10. It never leaves row 5, so its queen is locked to that row.
Teal: 4 squares across rows 10–12, columns 7–8.
Pale yellow covers 6 squares, spanning 6 rows and 1 column (rows 7–12, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Rose occupies 6 squares within rows 10–12, columns 8–11.
Blue: 9 squares across rows 3–8, columns 1–2.
Orange covers 9 squares, spanning 5 rows and 3 columns (rows 8–12, columns 10–12).
Indigo occupies 10 squares within rows 1–2, columns 1–6.
Sea green: 13 squares across rows 9–12, columns 2–6.
Amber covers 15 squares, spanning 5 rows and 5 columns (rows 1–5, columns 8–12).
Khaki occupies 16 squares within rows 5–9, columns 8–12.
Mint: 22 squares across rows 1–6, columns 2–11.
Red covers 32 squares, spanning 7 rows and 7 columns (rows 4–10, columns 3–9).
Where to start on this board
Open on the tightest color. Here that is slate, confined to 2 squares between rows 5 and 5 and columns 9 and 10. Its queen has nowhere else to go, which means those 1 row and 2 columns carry more constraint than anywhere else on #293.
Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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 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 #293
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2 and 3 are the narrowest, touched by only 3 colors. Columns 1, 7 and 12 are the tightest columns, 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 10 is the crowded extreme at 6 colors — worth revisiting later, not now.
Working through the middle game
The middle of #293 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
The whole middle game reduces to two sweeps. Sweep the twelve colors looking for one with a single square left; sweep the twelve rows and twelve columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 12x12 solve from a stalled one.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #293 is rated easy
The easy label comes out of four measurable things about #293: two of its regions are locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 3 colors, and its largest and smallest regions differ by 30. Boards that score tight on those measures give up their first queen fast.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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 #293 is row 1.
A non-spoiling distribution check: solved, #293 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 #293?
Puzzle #293 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #293 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #293, 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 #293?
Start with the slate region — the most constrained color on this board, with 2 squares spanning rows 5–5 and columns 9–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.