12x12 Queens Puzzle #278
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 #278
What follows is a complete solve of puzzle #278, 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 columns.
Show the full walkthrough (17 steps) — contains the solution
Step 1. Only row 1, column 7 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 7, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The amber region is down to one open square, at row 2, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 5, the remaining amber squares, and the ring of neighbours around row 2, column 5.
Step 3. Only row 10, column 6 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 6, in sea green and in the ring around that square is now dead.
Step 4. Wherever mint ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 4 — 3 of 12 queens placed. Step 5. Red is down to 3 candidates in rows 6 and 7, columns 8 and 9, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about red itself.
Step 6. All of the teal region's remaining squares (2 open squares) lie in row 11. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 9 squares come off.
Step 7. Only row 12, column 10 is still open in rose, and since each colour must take a queen, that settles it. Everything else in row 12, in column 10, in rose and in the ring around that square is now dead.
Step 8. The teal region is down to one open square, at row 11, column 8. Every colour holds exactly one queen, so that square is forced. Row 11 and column 8 are now spoken for, along with the squares touching that queen.
Step 9. Only row 6, column 9 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 9, the rest of the red region and every square adjacent to it — diagonals included.
The board after step 9 — 6 of 12 queens placed. Step 10. Wherever blue ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 11. Orange is down to 2 candidates in rows 7 and 9, columns 4 and 11, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about orange itself.
Step 12. Here is the pairing argument. The blue and pale yellow regions have no open squares outside columns 11 and 12 — 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: 1 square come off in one stroke.
Step 13. Only row 9, column 4 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 4, the rest of the orange region and every square adjacent to it — diagonals included.
The board after step 13 — 7 of 12 queens placed. Step 14. The mint region is down to one open square, at row 4, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 3, the remaining mint squares, and the ring of neighbours around row 4, column 3.
Step 15. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 1 square in all.
Step 16. Wherever slate ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 17. 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: khaki has one square left, so its queen takes row 8, column 2; slate has one square left, so its queen takes row 5, column 1; pale yellow has one square left, so its queen takes row 7, column 12; blue has one square left, so its queen takes row 3, 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 3, column 11.
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 #278
Board #278 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, #278 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 #278 are: indigo (1 square), sea green (3 squares), red (5 squares), rose (5 squares), amber (6 squares), teal (9 squares), slate (14 squares), pale yellow (16 squares), khaki (16 squares), mint (17 squares), blue (26 squares), orange (26 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the orange 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. Indigo has only 1 place to put its queen; orange 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.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×1 frame; mint is the loosest, occupying only 47% of its 6×6 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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 medium board.
Indigo occupies 1 square within rows 1–1, columns 7–7. It never leaves row 1, so its queen is locked to that row.
Sea green: 3 squares across rows 10–11, columns 5–6.
Red covers 5 squares, spanning 2 rows and 4 columns (rows 6–7, columns 6–9).
Rose occupies 5 squares within rows 11–12, columns 7–10.
Amber: 6 squares across rows 1–2, columns 4–7.
Teal covers 9 squares, spanning 3 rows and 5 columns (rows 10–12, columns 6–10).
Slate occupies 14 squares within rows 1–7, columns 1–3.
Pale yellow: 16 squares across rows 4–12, columns 11–12.
Khaki covers 16 squares, spanning 7 rows and 4 columns (rows 6–12, columns 1–4).
Mint occupies 17 squares within rows 1–6, columns 2–7.
Blue: 26 squares across rows 1–6, columns 6–12.
Orange covers 26 squares, spanning 6 rows and 9 columns (rows 7–12, columns 3–11).
Where to start on this board
Indigo is the natural opening on #278: it is the smallest region on the grid at 1 square, boxed into rows 1–1 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 indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Amber, red, sea green and rose 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 #278
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3, 8 and 9 are the narrowest, touched by only 3 colors. Columns 1 and 12 are the tightest columns, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 11 rows. By contrast row 11 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
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.
Keep alternating between two views of the board. In the region view you ask which of the twelve colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 12x12 board unwinds.
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 #278 is rated medium
The medium label comes out of four measurable things about #278: two 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 25. 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.
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 #278 the place to look for one is around column 1.
As a sanity check rather than a spoiler: the finished solution to #278 puts 4 queens on the outer border and 8 queens in the interior, with none in a 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 #278?
Puzzle #278 is rated medium. Its smallest color region holds 1 square, 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 #278 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #278, 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 #278?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.