12x12 Queens Puzzle #149
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 22-step reasoning is written out below.
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Step-by-step solution for puzzle #149
What follows is a complete solve of puzzle #149, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 12 queen placements and 10 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 confined to one line, last square in a region, region shadow, pairing argument on columns.
Show the full walkthrough (17 steps) — contains the solution
Step 1. Sea green cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to sea green, so every square in it owned by another colour is dead: 14 squares in all.
Step 2. All of the pale yellow 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: 10 squares come off.
Step 3. Rose cannot leave row 12 — every one of its open squares (4 open squares) sits there. That row belongs to rose, so every square on it owned by another colour is dead: 6 squares in all.
Step 4. 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: 10 squares come off.
The board after step 4 — 0 of 12 queens placed. Step 5. Only row 10, column 5 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 5, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 6. The khaki region has 3 squares left, spread across rows 8 and 9, columns 1 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 7. Orange cannot leave row 9 — every one of its open squares (5 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 3 squares in all.
Step 8. The khaki region is down to one open square, at row 8, column 1. Every colour holds exactly one queen, so that square is forced. Row 8 and column 1 are now spoken for, along with the squares touching that queen.
Step 9. Only row 7, column 6 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 6, the rest of the pale yellow region and every square adjacent to it — diagonals included.
The board after step 9 — 3 of 12 queens placed. Step 10. Wherever red 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 11. Amber, red, and teal 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 11 squares at once.
Step 12. All of the blue region's remaining squares (3 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 13. 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: orange has one square left, so its queen takes row 9, column 7; 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 11; blue has one square left, so its queen takes row 3, column 9; teal has one square left, so its queen takes row 11, column 12; red has one square left, so its queen takes row 6, column 10. 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 6, column 10.
The board after step 13 — 9 of 12 queens placed. Step 14. Wherever mint ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 15. The slate region is down to one open square, at row 5, column 4. Every colour holds exactly one queen, so that square is forced. Row 5 and column 4 are now spoken for, along with the squares touching that queen.
Step 16. Only row 4, column 2 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 2, the rest of the mint region and every square adjacent to it — diagonals included.
Step 17. The rose region is down to one open square, at row 12, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 12 and column 3, the remaining rose squares, and the ring of neighbours around row 12, column 3.
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 #149
Puzzle #149 is one of the easy-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.
Puzzle #149 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #149 are: sea green (2 squares), amber (4 squares), pale yellow (4 squares), rose (6 squares), indigo (7 squares), khaki (9 squares), teal (9 squares), blue (10 squares), red (16 squares), mint (21 squares), orange (23 squares), slate (33 squares). An even split would hand every color 12 squares, so the sea green region is running 10 squares under that average while the slate region is the roomiest area on the grid with 33 squares.
Every color takes one queen and one only, whatever its size — which is why the 31 square difference between sea green and slate 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.
Square count is only half the story — how a color is arranged counts too. Pale yellow is the tidiest shape on #149, packing 100% of its 2×2 bounding box, whereas blue straggles across its 5×4 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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.
Sea green occupies 2 squares within rows 10–11, columns 5–5. It sits wholly inside column 5, so its queen must be in that column.
Amber: 4 squares across rows 1–2, columns 10–12.
Pale yellow covers 4 squares, spanning 2 rows and 2 columns (rows 7–8, columns 5–6).
Rose occupies 6 squares within rows 11–12, columns 1–5.
Indigo: 7 squares across rows 1–3, columns 6–8.
Khaki covers 9 squares, spanning 4 rows and 3 columns (rows 8–11, columns 1–3).
Teal occupies 9 squares within rows 11–12, columns 6–12.
Blue: 10 squares across rows 1–5, columns 9–12.
Red covers 16 squares, spanning 6 rows and 5 columns (rows 4–9, columns 8–12).
Mint occupies 21 squares within rows 1–7, columns 1–5.
Orange: 23 squares across rows 7–11, columns 4–12.
Slate covers 33 squares, spanning 7 rows and 9 columns (rows 3–9, columns 2–10).
Where to start on this board
Open on the tightest color. Here that is sea green, confined to 2 squares between rows 10 and 11 and columns 5 and 5. Its queen has nowhere else to go, which means those 2 rows and 1 column carry more constraint than anywhere else on #149.
Because sea green stays inside column 5, its queen belongs to that column and no other region may use it. Cross out the rest of column 5 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
Work outward to the other flat regions next. Amber, pale yellow, rose and teal 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 #149
A quick way to find the next move is to count how many different colors touch each line. On this board, row 12 is the narrowest, touched by only 2 colors. Column 1 is the tightest column, 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 11 meets 5 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.
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.
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 #149 is rated easy
The easy label comes out of four measurable things about #149: one of its regions is locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 2 colors, and its largest and smallest regions differ by 31. Boards that score tight on those measures give up their first queen fast.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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 #149 is row 12.
As a sanity check rather than a spoiler: the finished solution to #149 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 #149?
Puzzle #149 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #149 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #149, 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 #149?
Start with the sea green region — the most constrained color on this board, with 2 squares spanning rows 10–11 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.