12x12 Queens Puzzle #66
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #66
What follows is a complete solve of puzzle #66, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 12 queen placements and 8 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 shadow, region confined to one line, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Only row 3, column 9 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 9, the rest of the blue region and every square adjacent to it — diagonals included.
Step 2. The rose region is down to one open square, at row 12, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 12 and column 1, the remaining rose squares, and the ring of neighbours around row 12, column 1.
Step 3. The khaki region has 4 squares left, spread across rows 8–10, columns 2 and 3. 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.
Step 4. All of the sea green region's remaining squares (2 open squares) lie in column 12. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 10 squares come off.
The board after step 4 — 2 of 12 queens placed. Step 5. Pale yellow is down to 4 candidates in rows 6–8, columns 10 and 11, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 6. Here is the pairing argument. The orange, sea green, and teal regions have no open squares outside rows 9–11 — 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: 6 squares come off in one stroke.
Step 7. Khaki cannot leave row 8 — every one of its open squares (2 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 7 squares in all.
Step 8. Red is down to 2 candidates in rows 6 and 7, columns 2 and 4, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about red itself.
The board after step 8 — 2 of 12 queens placed. Step 9. Red and pale yellow are now boxed into rows 6 and 7 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 7 squares at once.
Step 10. 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: slate has one square left, so its queen takes row 5, column 6; mint has one square left, so its queen takes row 4, column 4; red has one square left, so its queen takes row 6, column 2; khaki has one square left, so its queen takes row 8, 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 8, column 3.
Step 11. Here is the pairing argument. The pale yellow and orange regions have no open squares outside columns 10 and 11 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 3 squares come off in one stroke.
Step 12. 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: indigo has one square left, so its queen takes row 1, column 8; amber has one square left, so its queen takes row 2, column 5; teal has one square left, so its queen takes row 11, column 7; sea green has one square left, so its queen takes row 10, column 12; 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 11. 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 11.
The board after step 12 — 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 #66
Board #66 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.
As with every puzzle in this collection, #66 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 #66 are: blue (1 square), rose (1 square), sea green (3 squares), pale yellow (9 squares), khaki (9 squares), slate (11 squares), orange (11 squares), mint (12 squares), red (15 squares), amber (23 squares), teal (23 squares), indigo (26 squares). An even split would hand every color 12 squares, so the blue region is running 11 squares under that average while the indigo region is the roomiest area on the grid with 26 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 blue, with 1 square, is under far more pressure than indigo with 26. A 25-square gap like this one rewards players who start where the choices are fewest.
A region's outline can constrain it more than its size does. Here blue is the most solid, filling 100% of its 1×1 box, and red the most diffuse at 36% of its 7×6 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.
Blue: 1 square across rows 3–3, columns 9–9. It never leaves row 3, 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.
Sea green occupies 3 squares within rows 10–12, columns 12–12. It sits wholly inside column 12, so its queen must be in that column.
Pale yellow: 9 squares across rows 4–8, columns 10–12.
Khaki covers 9 squares, spanning 5 rows and 3 columns (rows 8–12, columns 1–3).
Slate occupies 11 squares within rows 5–10, columns 5–9.
Orange: 11 squares across rows 8–12, columns 9–12.
Mint covers 12 squares, spanning 4 rows and 5 columns (rows 3–6, columns 3–7).
Red occupies 15 squares within rows 4–10, columns 1–6.
Amber: 23 squares across rows 1–5, columns 1–7.
Teal covers 23 squares, spanning 4 rows and 7 columns (rows 9–12, columns 3–9).
Indigo occupies 26 squares within rows 1–6, columns 7–12.
Where to start on this board
Blue is the natural opening on #66: it is the smallest region on the grid at 1 square, boxed into rows 3–3 and columns 9–9. 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 blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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 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 #66
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, 8, 10 and 11 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 11 rows. By contrast row 10 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #66 is rated medium
Ratings track how generous the opening is. On #66 you get five 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 medium label.
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.
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 #66, start hunting for it near row 1.
As a sanity check rather than a spoiler: the finished solution to #66 puts 3 queens on the outer border and 9 queens in the interior, 1 of them in an actual corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #66?
Puzzle #66 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #66 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #66, 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 #66?
Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.