12x12 Queens Puzzle #277
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #277
What follows is a complete solve of puzzle #277, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 12 queen placements and 7 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 confined to one line, region shadow, pairing argument on rows.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 10, column 11 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 11, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 2. The rose region is down to one open square, at row 12, column 12. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 12 and column 12, the remaining rose squares, and the ring of neighbours around row 12, column 12.
Step 3. Indigo cannot leave row 1 — every one of its open squares (5 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 5 squares in all.
Step 4. All of the slate 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: 7 squares come off.
The board after step 4 — 2 of 12 queens placed. Step 5. Only row 6, column 8 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 8, the rest of the red region and every square adjacent to it — diagonals included.
Step 6. The slate region is down to one open square, at row 5, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 10, the remaining slate squares, and the ring of neighbours around row 5, column 10.
Step 7. Khaki cannot leave column 9 — every one of its open squares (2 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 3 squares in all.
Step 8. Amber is down to 4 candidates in rows 2, 4, and 7, columns 6 and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 9. Khaki, orange, and teal are now boxed into rows 8, 9, and 11 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 6 squares at once.
The board after step 9 — 4 of 12 queens placed. Step 10. The pale yellow region is down to one open square, at row 7, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 5, the remaining pale yellow squares, and the ring of neighbours around row 7, column 5.
Step 11. Amber is down to 3 candidates in rows 2 and 4, columns 6 and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 12. All of the mint region's remaining squares (2 open squares) lie in row 4. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 13. 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: amber has one square left, so its queen takes row 2, column 7; indigo has one square left, so its queen takes row 1, column 4; mint has one square left, so its queen takes row 4, column 3; blue has one square left, so its queen takes row 3, column 1; teal has one square left, so its queen takes row 11, column 6; orange has one square left, so its queen takes row 9, column 2; khaki has one square left, so its queen takes row 8, column 9. 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 9.
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 #277
Puzzle #277 is one of the medium-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.
There is exactly one way to finish #277, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these twelve regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #277 are: sea green (1 square), red (2 squares), indigo (5 squares), rose (7 squares), pale yellow (10 squares), slate (12 squares), khaki (12 squares), orange (15 squares), blue (16 squares), mint (17 squares), teal (20 squares), amber (27 squares). An even split would hand every color 12 squares, so the sea green region is running 11 squares under that average while the amber region is the roomiest area on the grid with 27 squares.
Every color takes one queen and one only, whatever its size — which is why the 26 square difference between sea green and amber 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.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×5 frame; mint is the loosest, occupying only 40% of its 6×7 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Below is every color on #277 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.
Sea green covers 1 square, spanning 1 row and 1 column (rows 10–10, columns 11–11). It never leaves row 10, so its queen is locked to that row.
Red occupies 2 squares within rows 6–6, columns 8–9. It never leaves row 6, so its queen is locked to that row.
Indigo: 5 squares across rows 1–1, columns 4–8. It never leaves row 1, so its queen is locked to that row.
Rose covers 7 squares, spanning 4 rows and 3 columns (rows 9–12, columns 10–12).
Pale yellow occupies 10 squares within rows 6–9, columns 3–7.
Slate: 12 squares across rows 4–8, columns 10–12.
Khaki covers 12 squares, spanning 4 rows and 4 columns (rows 7–10, columns 8–11).
Orange occupies 15 squares within rows 8–12, columns 1–4.
Blue: 16 squares across rows 1–5, columns 1–6.
Mint covers 17 squares, spanning 6 rows and 7 columns (rows 3–8, columns 1–7).
Teal occupies 20 squares within rows 8–12, columns 4–10.
Amber: 27 squares across rows 1–7, columns 6–12.
Where to start on this board
Open on the tightest color. Here that is sea green, confined to 1 square between rows 10 and 10 and columns 11 and 11. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #277.
Because sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. 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 and red 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 #277
A quick way to find the next move is to count how many different colors touch each line. On this board, row 2 is the narrowest, touched by only 2 colors. Columns 1, 2 and 12 are the tightest columns, 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 6 colors crossing it; it will almost certainly be among the last to settle.
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.
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 #277 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 #277 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 26. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
Stuck on #277 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 #277 is row 2.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 9 queens in the middle, including 1 in a corner. 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 #277?
Puzzle #277 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #277 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #277, 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 #277?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.