12x12 Queens Puzzle #242
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 26-step reasoning is written out below.
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Step-by-step solution for puzzle #242
What follows is a complete solve of puzzle #242, worked the way a person works it rather than the way a computer does. It runs to 26 deductions — 12 queen placements and 14 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 proof by contradiction.
Techniques this board needs: last square in a region, region confined to one line, region shadow, line confined to one region, pairing argument on columns, pairing argument on rows, proof by contradiction, last square in a row.
Show the full walkthrough (19 steps) — contains the solution
Step 1. Only row 12, column 8 is still open in rose, and since each colour must take a queen, that settles it. That clears row 12, column 8, the rest of the rose region and every square adjacent to it — diagonals included.
Step 2. The sea green region is down to one open square, at row 10, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 7, the remaining sea green squares, and the ring of neighbours around row 10, column 7.
Step 3. Indigo cannot leave row 1 — every one of its open squares (4 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 6 squares in all.
Step 4. Wherever amber 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 5. Mint is down to 5 candidates in rows 2–5, columns 1–3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
The board after step 5 — 2 of 12 queens placed. Step 6. Every open square left in column 6 (7 open squares) belongs to the red region. Since that column must contain a queen, red is the colour that supplies it — so red squares anywhere else on the board are out, 22 squares in all.
Step 7. Amber, mint, and teal are now boxed into columns 1–3 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 8. Here is the pairing argument. The amber, blue, mint, and slate regions have no open squares outside rows 2–5 — 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: 4 squares come off in one stroke.
Step 9. Test row 1, column 9 for indigo: place a queen there, run the forced consequences through, and the mint region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 10. All of the indigo region's remaining squares (3 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
The board after step 10 — 2 of 12 queens placed. Step 11. Test row 1, column 12 for indigo: place a queen there, run the forced consequences through, and the mint region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 12. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 13. Test row 3, column 1 for amber: place a queen there, run the forced consequences through, and the orange region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 14. Amber is down to 2 candidates in rows 2 and 3, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
The board after step 14 — 2 of 12 queens placed. Step 15. Test row 3, column 2 for amber: place a queen there, run the forced consequences through, and the pale yellow region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 16. The amber region is down to one open square, at row 2, column 1. Every colour holds exactly one queen, so that square is forced. Row 2 and column 1 are now spoken for, along with the squares touching that queen.
Step 17. Look along row 5: one square survives, row 5, column 4, which belongs to slate. A row cannot be left empty, so the queen goes there. Everything else in row 5, in column 4, in slate and in the ring around that square is now dead.
Step 18. 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: 4 squares come off.
Step 19. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: orange has one square left, so its queen takes row 9, column 9; khaki has one square left, so its queen takes row 8, column 5; red has one square left, so its queen takes row 6, column 6; 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 10; indigo has one square left, so its queen takes row 1, column 11; mint has one square left, so its queen takes row 4, column 2; teal has one square left, so its queen takes row 11, column 3. 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 11, column 3.
The board after step 19 — 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 #242
Board #242 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, #242 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 #242 are: rose (1 square), indigo (5 squares), pale yellow (5 squares), sea green (5 squares), amber (6 squares), mint (7 squares), orange (13 squares), blue (15 squares), slate (15 squares), teal (16 squares), khaki (17 squares), red (39 squares). An even split would hand every color 12 squares, so the rose region is running 11 squares under that average while the red region is the roomiest area on the grid with 39 squares.
Every color takes one queen and one only, whatever its size — which is why the 38 square difference between rose and red 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; slate is the loosest, occupying only 43% of its 7×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Rose occupies 1 square within rows 12–12, columns 8–8. It never leaves row 12, so its queen is locked to that row.
Indigo: 5 squares across rows 1–1, columns 8–12. It never leaves row 1, so its queen is locked to that row.
Pale yellow covers 5 squares, spanning 4 rows and 2 columns (rows 6–9, columns 11–12).
Sea green occupies 5 squares within rows 10–12, columns 7–8.
Amber: 6 squares across rows 1–3, columns 1–3.
Mint covers 7 squares, spanning 4 rows and 3 columns (rows 2–5, columns 1–3).
Orange occupies 13 squares within rows 9–12, columns 8–12.
Blue: 15 squares across rows 1–4, columns 6–12.
Slate covers 15 squares, spanning 7 rows and 5 columns (rows 1–7, columns 1–5).
Teal occupies 16 squares within rows 8–12, columns 1–6.
Khaki: 17 squares across rows 7–11, columns 1–7.
Red covers 39 squares, spanning 9 rows and 9 columns (rows 2–10, columns 4–12).
Where to start on this board
Rose is the natural opening on #242: it is the smallest region on the grid at 1 square, boxed into rows 12–12 and columns 8–8. 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 rose never leaves row 12, its queen must be in that row — and that instantly settles row 12 for everyone else. Sweep along it and X out every square that is not rose. 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 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 #242
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5 and 6 are the narrowest, touched by only 3 colors. Columns 4, 5, 6, 7, 9 and 10 are the tightest columns, with 4 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 11 rows. Row 10, meeting 5 colors, is the opposite case — the busiest line on #242 and the last one you should expect to crack.
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.
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 #242 is rated easy
Ratings track how generous the opening is. On #242 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 38-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
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.
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.
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 #242 is row 5.
Here is a shape check that gives nothing away: when #242 is solved, 4 queens sit on the outer edge of the grid and 8 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #242?
Puzzle #242 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #242 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #242, 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 #242?
Start with the rose region — the most constrained color on this board, with 1 square spanning rows 12–12 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.