12x12 Queens Puzzle #204
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #204
What follows is a complete solve of puzzle #204, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 12 queen placements and 8 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 line confined to one region.
Techniques this board needs: last square in a region, region shadow, region confined to one line, line confined to one region, last square in a row.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 12, column 1 is still open in rose, and since each colour must take a queen, that settles it. That clears row 12, column 1, the rest of the rose region and every square adjacent to it — diagonals included.
Step 2. The teal region is down to one open square, at row 11, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 5, the remaining teal squares, and the ring of neighbours around row 11, column 5.
Step 3. Only row 10, column 3 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 3, in sea green and in the ring around that square is now dead.
Step 4. Wherever blue ends up among its 3 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
Step 5. Slate cannot leave column 12 — every one of its open squares (3 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 7 squares in all.
The board after step 5 — 3 of 12 queens placed. Step 6. The khaki region is down to one open square, at row 8, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 11, the remaining khaki squares, and the ring of neighbours around row 8, column 11.
Step 7. Only row 1, column 10 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 10, in indigo and in the ring around that square is now dead.
Step 8. Red is down to 3 candidates in rows 6 and 7, columns 8 and 9, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about red itself.
Step 9. The mint region has 4 squares left, spread across rows 4 and 5, columns 7–9. 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 — 5 of 12 queens placed. Step 10. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 11. Pale yellow cannot leave column 2 — every one of its open squares (3 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 2 squares in all.
Step 12. Every open square left in row 2 (2 open squares) belongs to the amber region. Since that row must contain a queen, amber is the colour that supplies it — so amber squares anywhere else on the board are out, 3 squares in all.
Step 13. Row 9 has only orange squares left (4 open squares). The row needs a queen and only orange can provide one, which pins that colour to this row and kills its squares elsewhere: 6 squares.
Step 14. 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: row 6 is down to one square, putting a queen on row 6, column 8; blue has one square left, so its queen takes row 3, column 7; amber has one square left, so its queen takes row 2, column 4; mint has one square left, so its queen takes row 4, column 9; slate has one square left, so its queen takes row 5, column 12; pale yellow has one square left, so its queen takes row 7, column 2; orange has one square left, so its queen takes row 9, column 6. 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 6.
The board after step 14 — 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 #204
This is puzzle number 204 in the 12x12 collection, rated medium. The grid holds 144 squares split between twelve colored regions, and a finished board carries twelve queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
As with every puzzle in this collection, #204 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 #204 are: rose (1 square), teal (2 squares), blue (3 squares), slate (3 squares), red (3 squares), indigo (5 squares), sea green (7 squares), khaki (14 squares), pale yellow (20 squares), mint (24 squares), amber (28 squares), orange (34 squares). An even split would hand every color 12 squares, so the rose region is running 11 squares under that average while the orange region is the roomiest area on the grid with 34 squares.
Every color takes one queen and one only, whatever its size — which is why the 33 square difference between rose and orange 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. Slate is the tidiest shape on #204, packing 100% of its 3×1 bounding box, whereas pale yellow straggles across its 8×5 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #204, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Rose: 1 square across rows 12–12, columns 1–1. It never leaves row 12, so its queen is locked to that row.
Teal covers 2 squares, spanning 2 rows and 1 column (rows 11–12, columns 5–5). It sits wholly inside column 5, so its queen must be in that column.
Blue occupies 3 squares within rows 3–4, columns 7–8.
Slate: 3 squares across rows 3–5, columns 12–12. It sits wholly inside column 12, so its queen must be in that column.
Red covers 3 squares, spanning 2 rows and 2 columns (rows 6–7, columns 8–9).
Indigo occupies 5 squares within rows 1–2, columns 10–12.
Sea green: 7 squares across rows 10–12, columns 2–4.
Khaki covers 14 squares, spanning 7 rows and 3 columns (rows 6–12, columns 10–12).
Pale yellow occupies 20 squares within rows 4–11, columns 1–5.
Mint: 24 squares across rows 2–9, columns 7–11.
Amber covers 28 squares, spanning 5 rows and 9 columns (rows 1–5, columns 1–9).
Orange occupies 34 squares within rows 5–12, columns 2–9.
Where to start on this board
The most constrained color is where a solve should begin, and on #204 that is rose with 1 square. It reaches from row 12 to row 12 and from column 1 to column 1 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on 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, blue, red 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 #204
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Column 6 is the tightest column, with 2 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 12 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.
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.
With twelve queens to seat and twelve regions competing over 144 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 12x12 boards quickly and players who stall halfway.
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 #204 is rated medium
The rating reflects how much the board concedes up front. Puzzle #204 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 33 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
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 #204 is row 1.
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 #204?
Puzzle #204 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 #204 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #204, 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 #204?
Start with the rose region — the most constrained color on this board, with 1 square spanning rows 12–12 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.