12x12 Queens Puzzle #218
Difficulty: medium. 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 #218
What follows is a complete solve of puzzle #218, 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 shadow, pairing argument on rows, region confined to one line.
Show the full walkthrough (8 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: mint has one square left, so its queen takes row 4, column 5; khaki has one square left, so its queen takes row 8, column 11; indigo has one square left, so its queen takes row 1, column 12; rose has one square left, so its queen takes row 12, column 1; teal has one square left, so its queen takes row 11, column 7. 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 7.
Step 2. The red region has 3 squares left, spread across rows 5 and 6, 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 3. Wherever pale yellow ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 4. Here is the pairing argument. The amber and blue regions have no open squares outside rows 2 and 3 — 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: 2 squares come off in one stroke.
The board after step 4 — 5 of 12 queens placed. Step 5. Slate cannot leave row 5 — every one of its open squares (3 open squares) sits there. That row belongs to slate, so every square on it owned by another colour is dead: 2 squares in all.
Step 6. The red region is down to one open square, at row 6, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 2, the remaining red squares, and the ring of neighbours around row 6, column 2.
Step 7. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 2 squares in all.
Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: sea green has one square left, so its queen takes row 10, column 3; amber has one square left, so its queen takes row 2, column 4; blue has one square left, so its queen takes row 3, column 9; pale yellow has one square left, so its queen takes row 7, column 8; slate has one square left, so its queen takes row 5, column 10; orange has one square left, so its queen takes row 9, column 6. 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 9, column 6.
The board after step 8 — 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 #218
Board #218 of the 12x12 bank carries a medium 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.
Like every board on this site, #218 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #218 are: mint (1 square), khaki (1 square), rose (1 square), indigo (2 squares), pale yellow (8 squares), teal (8 squares), red (12 squares), blue (15 squares), amber (17 squares), slate (23 squares), orange (28 squares), sea green (28 squares). An even split would hand every color 12 squares, so the mint region is running 11 squares under that average while the sea green region is the roomiest area on the grid with 28 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 sea green with 28. A 27-square gap like this one rewards players who start where the choices are fewest.
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 orange is the most scattered at 47% of its 6×10 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
Below is every color on #218 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 occupies 1 square within rows 4–4, columns 5–5. It never leaves row 4, so its queen is locked to that row.
Khaki: 1 square across rows 8–8, columns 11–11. It never leaves row 8, so its queen is locked to that row.
Rose covers 1 square, spanning 1 row and 1 column (rows 12–12, columns 1–1). It never leaves row 12, so its queen is locked to that row.
Indigo occupies 2 squares within rows 1–1, columns 11–12. It never leaves row 1, so its queen is locked to that row.
Pale yellow: 8 squares across rows 6–8, columns 7–10.
Teal covers 8 squares, spanning 2 rows and 7 columns (rows 11–12, columns 6–12).
Red occupies 12 squares within rows 4–8, columns 1–5.
Blue: 15 squares across rows 1–4, columns 6–10.
Amber covers 17 squares, spanning 4 rows and 5 columns (rows 1–4, columns 1–5).
Slate occupies 23 squares within rows 2–7, columns 6–12.
Orange: 28 squares across rows 6–11, columns 3–12.
Sea green covers 28 squares, spanning 7 rows and 6 columns (rows 6–12, columns 1–6).
Where to start on this board
Mint is the natural opening on #218: it is the smallest region on the grid at 1 square, boxed into rows 4–4 and columns 5–5. 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, khaki, rose and teal 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 #218
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5, 9 and 10 are the narrowest, touched by only 2 colors. Column 2 is the tightest column, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 11 rows. Row 8 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
Two checks, run alternately, will carry you through the 144 squares of this grid. First: has any of the twelve regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 12x12 boards almost always run one of those checks and forget the other.
Resist the plausible-looking queen. On #218 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 #218 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers seven single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 27. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
If #218 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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 #218, start hunting for it near row 5.
Use this as a rough check on your progress: the completed board has 2 queens around the border and 10 queens in the middle, including 2 in corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #218?
Puzzle #218 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and seven of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #218 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #218, 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 #218?
Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.