12x12 Queens Puzzle #214
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.
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Step-by-step solution for puzzle #214
What follows is a complete solve of puzzle #214, 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 pairing argument on columns.
Techniques this board needs: last square in a region, region confined to one line, pairing argument on rows, region shadow, pairing argument on columns.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 8, column 7 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 7, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 2. The red region is down to one open square, at row 6, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 8, the remaining red squares, and the ring of neighbours around row 6, column 8.
Step 3. Rose cannot leave row 12 — every one of its open squares (3 open squares) sits there. That row belongs to rose, so every square on it owned by another colour is dead: 8 squares in all.
Step 4. Here is the pairing argument. The pale yellow, orange, sea green, and teal regions have no open squares outside rows 7, 9, 10, and 11 — 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: 5 squares come off in one stroke.
The board after step 4 — 2 of 12 queens placed. Step 5. Mint is down to 5 candidates in rows 3–5, columns 1–3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 6. All of the slate region's remaining squares (2 open squares) lie in row 5. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 9 squares come off.
Step 7. Mint cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 7 squares in all.
Step 8. The teal region is down to one open square, at row 11, column 2. Every colour holds exactly one queen, so that square is forced. Row 11 and column 2 are now spoken for, along with the squares touching that queen.
Step 9. The orange region has 4 squares left, spread across rows 7, 9, and 10, columns 3–5. 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 9 — 3 of 12 queens placed. Step 10. All of the sea green region's remaining squares (2 open squares) lie in row 10. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 11. Indigo, slate, pale yellow, and rose are now boxed into columns 9–12 and nothing else. That is 4 colours needing 4 columns, so they fill those columns between them — which locks every remaining colour out and removes 8 squares at once.
Step 12. All of the blue region's remaining squares (2 open squares) lie in column 6. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
Step 13. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: sea green has one square left, so its queen takes row 10, column 5; orange has one square left, so its queen takes row 9, column 3; pale yellow has one square left, so its queen takes row 7, column 11; slate has one square left, so its queen takes row 5, column 10; rose has one square left, so its queen takes row 12, column 12; indigo has one square left, so its queen takes row 1, column 9; blue has one square left, so its queen takes row 3, column 6; mint has one square left, so its queen takes row 4, column 1; amber has one square left, so its queen takes row 2, column 4. 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 4.
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 #214
Board #214 of the 12x12 bank carries a easy 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.
As with every puzzle in this collection, #214 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 #214 are: khaki (1 square), rose (3 squares), red (5 squares), indigo (7 squares), teal (9 squares), mint (10 squares), slate (10 squares), orange (14 squares), pale yellow (17 squares), sea green (17 squares), blue (22 squares), amber (29 squares). An even split would hand every color 12 squares, so the khaki region is running 11 squares under that average while the amber region is the roomiest area on the grid with 29 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Khaki has only 1 place to put its queen; amber has 29. The spread between them on this board is 28 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 khaki is the most solid, filling 100% of its 1×1 box, and teal the most diffuse at 50% of its 6×3 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
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.
Khaki covers 1 square, spanning 1 row and 1 column (rows 8–8, columns 7–7). It never leaves row 8, so its queen is locked to that row.
Rose occupies 3 squares within rows 12–12, columns 10–12. It never leaves row 12, so its queen is locked to that row.
Red: 5 squares across rows 6–8, columns 6–8.
Indigo covers 7 squares, spanning 2 rows and 5 columns (rows 1–2, columns 8–12).
Teal occupies 9 squares within rows 7–12, columns 1–3.
Mint: 10 squares across rows 3–7, columns 1–3.
Slate covers 10 squares, spanning 4 rows and 4 columns (rows 5–8, columns 9–12).
Orange occupies 14 squares within rows 7–12, columns 2–5.
Pale yellow: 17 squares across rows 7–11, columns 8–12.
Sea green covers 17 squares, spanning 5 rows and 5 columns (rows 8–12, columns 5–9).
Blue occupies 22 squares within rows 1–5, columns 6–12.
Amber: 29 squares across rows 1–7, columns 1–7.
Where to start on this board
Khaki is the natural opening on #214: it is the smallest region on the grid at 1 square, boxed into rows 8–8 and columns 7–7. 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 khaki never leaves row 8, its queen must be in that row — and that instantly settles row 8 for everyone else. Sweep along it and X out every square that is not khaki. 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. Rose and indigo 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 #214
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3 and 4 are the narrowest, touched by only 3 colors. Column 4 is the tightest column, with 2 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 8 is the crowded extreme at 7 colors — worth revisiting later, not now.
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.
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 #214 is rated easy
The easy label comes out of four measurable things about #214: three 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 28. 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 easy board from the rest.
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.
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 #214 the place to look for one is around column 4.
A non-spoiling distribution check: solved, #214 carries 3 queens on the perimeter against 9 queens inside, 1 of them cornered. 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 #214?
Puzzle #214 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #214 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #214, 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 #214?
Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.