12x12 Queens Puzzle #247
Difficulty: hard. 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 #247
What follows is a complete solve of puzzle #247, 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 columns.
Techniques this board needs: region shadow, pairing argument on rows, pairing argument on columns, last square in a region, region confined to one line, line confined to one region, last square in a column.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Wherever indigo ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. Amber is down to 3 candidates in rows 1 and 2, columns 11 and 12, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The orange region has 4 squares left, spread across rows 8 and 9, columns 8–10. 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 3 — 0 of 12 queens placed. Step 4. Here is the pairing argument. The indigo, amber, blue, and mint regions have no open squares outside rows 1–4 — 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: 19 squares come off in one stroke.
Step 5. Amber, mint, and khaki are now boxed into columns 10–12 and nothing else. That is 3 colours needing 3 columns, so they fill those columns between them — which locks every remaining colour out and removes 10 squares at once.
Step 6. 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: teal has one square left, so its queen takes row 11, column 9; orange has one square left, so its queen takes row 9, column 8; indigo has one square left, so its queen takes row 1, column 7; amber has one square left, so its queen takes row 2, column 11; mint has one square left, so its queen takes row 4, column 10; rose has one square left, so its queen takes row 12, column 6; slate has one square left, so its queen takes row 5, column 5. 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 5, column 5.
The board after step 6 — 7 of 12 queens placed. Step 7. Red cannot leave row 6 — every one of its open squares (2 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 4 squares in all.
Step 8. Every open square left in column 4 (3 open squares) belongs to the sea green region. Since that column must contain a queen, sea green is the colour that supplies it — so sea green squares anywhere else on the board are out, 3 squares in all.
Step 9. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: column 3 is down to one square, putting a queen on row 7, column 3; red has one square left, so its queen takes row 6, column 1; blue has one square left, so its queen takes row 3, column 2; sea green has one square left, so its queen takes row 10, column 4; khaki has one square left, so its queen takes row 8, column 12. 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 12.
The board after step 9 — 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 #247
12x12 puzzle #247 is rated hard. Twelve colored regions cover its 144 squares, and your job is to seat twelve queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
There is exactly one way to finish #247, 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 #247 are: amber (3 squares), orange (4 squares), indigo (5 squares), mint (6 squares), teal (7 squares), pale yellow (8 squares), rose (9 squares), blue (13 squares), khaki (14 squares), red (19 squares), slate (27 squares), sea green (29 squares). An even split would hand every color 12 squares, so the amber region is running 9 squares under that average while the sea green 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. Amber has only 3 places to put its queen; sea green has 29. The spread between them on this board is 26 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 teal is the most solid, filling 78% of its 3×3 box, and slate the most diffuse at 48% of its 7×8 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #247 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.
Amber covers 3 squares, spanning 2 rows and 2 columns (rows 1–2, columns 11–12).
Orange occupies 4 squares within rows 8–9, columns 8–10.
Indigo: 5 squares across rows 1–3, columns 7–9.
Mint covers 6 squares, spanning 4 rows and 2 columns (rows 1–4, columns 10–11).
Teal occupies 7 squares within rows 10–12, columns 9–11.
Pale yellow: 8 squares across rows 6–10, columns 1–3.
Rose covers 9 squares, spanning 3 rows and 5 columns (rows 10–12, columns 6–10).
Blue occupies 13 squares within rows 1–4, columns 1–6.
Khaki: 14 squares across rows 6–12, columns 10–12.
Red covers 19 squares, spanning 5 rows and 6 columns (rows 2–6, columns 1–6).
Slate occupies 27 squares within rows 2–8, columns 5–12.
Sea green: 29 squares across rows 7–12, columns 1–7.
Where to start on this board
Begin where the choices are fewest. On this board that means amber, which owns just 3 squares inside a 2×2 window running from row 1 to row 2 and column 11 to column 12. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Amber spans 2 rows, so it stays open for now — but it is still the shortest list on the board at 3 squares. Work through those squares first and mark the ones that would leave another region homeless. That pruning is what makes the rest of the grid legible.
Work outward to the other flat regions next. Orange 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 #247
A quick way to find the next move is to count how many different colors touch each line. On this board, row 5 is the narrowest, touched by only 2 colors. Columns 4 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 2 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
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.
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 #247 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers no single-line region at all, a 3-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.
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.
Stuck on #247 despite the hard 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.
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 #247 the place to look for one is around row 5.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 8 queens in the middle, and nothing in the 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 #247?
Puzzle #247 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 2 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 12x12 puzzle #247 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #247, 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 #247?
Start with the amber region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 11–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.