12x12 Queens Puzzle #282
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 23-step reasoning is written out below.
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Step-by-step solution for puzzle #282
What follows is a complete solve of puzzle #282, worked the way a person works it rather than the way a computer does. It runs to 23 deductions — 12 queen placements and 11 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 confined to one line, region shadow, pairing argument on rows, pairing argument on columns, last square in a row, last square in a column.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 2, column 4 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 4, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (5 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
Step 3. The orange region has 3 squares left, spread across rows 9 and 10, columns 1 and 2. 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. Wherever red 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.
The board after step 4 — 1 of 12 queens placed. Step 5. Teal is down to 4 candidates in rows 10 and 11, columns 10–12, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about teal itself.
Step 6. All of the rose region's remaining squares (2 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 13 squares come off.
Step 7. Orange, sea green, teal, and rose are now boxed into rows 9–12 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 20 squares at once.
Step 8. Here is the pairing argument. The red, pale yellow, and khaki regions have no open squares outside rows 6–8 — 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 9. The slate region has 5 squares left, spread across rows 3–5, columns 10–12. 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 9 — 1 of 12 queens placed. Step 10. Here is the pairing argument. The red and orange regions have no open squares outside columns 1 and 2 — 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: 7 squares come off in one stroke.
Step 11. Mint cannot leave column 3 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 3 squares in all.
Step 12. Here is the pairing argument. The slate, pale yellow, and teal regions have no open squares outside columns 10–12 — 3 colours confined to 3 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 10 squares come off in one stroke.
Step 13. From here the board cascades. Keep alternating the region sweep and the line sweep and 11 queens fall out in order without any new idea being needed: indigo has one square left, so its queen takes row 1, column 9; sea green has one square left, so its queen takes row 10, column 7; teal has one square left, so its queen takes row 11, column 12; rose has one square left, so its queen takes row 12, column 8; row 3 is down to one square, putting a queen on row 3, column 6; row 4 is down to one square, putting a queen on row 4, column 3; row 8 is down to one square, putting a queen on row 8, column 5; column 10 is down to one square, putting a queen on row 5, column 10; pale yellow has one square left, so its queen takes row 7, column 11; red has one square left, so its queen takes row 6, column 1; orange has one square left, so its queen takes row 9, column 2. 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 9, column 2.
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 #282
Board #282 of the 12x12 bank carries a easy 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, #282 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 #282 are: amber (1 square), rose (2 squares), orange (3 squares), red (4 squares), teal (4 squares), indigo (5 squares), pale yellow (8 squares), slate (12 squares), sea green (15 squares), mint (17 squares), blue (32 squares), khaki (41 squares). An even split would hand every color 12 squares, so the amber region is running 11 squares under that average while the khaki region is the roomiest area on the grid with 41 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 1 place to put its queen; khaki has 41. The spread between them on this board is 40 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 1×5 frame; slate is the loosest, occupying only 43% of its 7×4 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 #282 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: 1 square across rows 2–2, columns 4–4. It never leaves row 2, so its queen is locked to that row.
Rose covers 2 squares, spanning 2 rows and 1 column (rows 11–12, columns 8–8). It sits wholly inside column 8, so its queen must be in that column.
Orange occupies 3 squares within rows 9–10, columns 1–2.
Red: 4 squares across rows 6–8, columns 1–2.
Teal covers 4 squares, spanning 2 rows and 3 columns (rows 10–11, columns 10–12).
Indigo occupies 5 squares within rows 1–1, columns 8–12. It never leaves row 1, so its queen is locked to that row.
Pale yellow: 8 squares across rows 6–9, columns 10–12.
Slate covers 12 squares, spanning 7 rows and 4 columns (rows 2–8, columns 9–12).
Sea green occupies 15 squares within rows 8–12, columns 7–12.
Mint: 17 squares across rows 1–6, columns 1–4.
Blue covers 32 squares, spanning 5 rows and 8 columns (rows 1–5, columns 4–11).
Khaki occupies 41 squares within rows 6–12, columns 1–9.
Where to start on this board
Amber is the natural opening on #282: it is the smallest region on the grid at 1 square, boxed into rows 2–2 and columns 4–4. 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 amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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, orange, teal 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 #282
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3, 4, 5 and 12 are the narrowest, touched by only 3 colors. Columns 3, 5 and 6 are the tightest columns, with 2 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 11 rows. Row 8 is the crowded extreme at 5 colors — worth revisiting later, not now.
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.
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 #282 is rated easy
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 3 colors, and a region-size spread of 40. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a easy board from the rest.
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 #282 the place to look for one is around column 3.
A non-spoiling distribution check: solved, #282 carries 4 queens on the perimeter against 8 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
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 #282?
Puzzle #282 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #282 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #282, 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 #282?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.