12x12 Queens Puzzle #205
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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #205
What follows is a complete solve of puzzle #205, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 12 queen placements and 9 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 shadow, pairing argument on rows, pairing argument on columns, last square in a row, region confined to one line.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Only row 1, column 7 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 7, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The rose region is down to one open square, at row 12, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 12 and column 1, the remaining rose squares, and the ring of neighbours around row 12, column 1.
Step 3. The amber region has 4 squares left, spread across rows 2–4, columns 4 and 5. 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.
Step 4. Wherever blue 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. Red is down to 4 candidates in rows 4–6, columns 4 and 5, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about red itself.
The board after step 5 — 2 of 12 queens placed. Step 6. Here is the pairing argument. The amber and blue regions have no open squares outside rows 2 and 3 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 9 squares come off in one stroke.
Step 7. Mint, slate, and red are now boxed into rows 4–6 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 11 squares at once.
Step 8. Here is the pairing argument. The amber and red regions have no open squares outside columns 4 and 5 — 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: 10 squares come off in one stroke.
Step 9. The sea green region has 3 squares left, spread across rows 7 and 10, columns 2 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 10. Row 6 has a single open square left, at column 5 in the red region. Every row needs a queen, so this one is forced. Row 6 and column 5 are now spoken for, along with the squares touching that queen.
The board after step 10 — 3 of 12 queens placed. Step 11. Only row 2, column 4 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 4, in amber and in the ring around that square is now dead.
Step 12. The blue region is down to one open square, at row 3, column 11. Every colour holds exactly one queen, so that square is forced. Row 3 and column 11 are now spoken for, along with the squares touching that queen.
Step 13. Slate and sea green are now boxed into columns 2 and 3 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 5 squares at once.
Step 14. All of the teal 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: 3 squares come off.
Step 15. 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: pale yellow has one square left, so its queen takes row 7, column 8; mint has one square left, so its queen takes row 4, column 9; sea green has one square left, so its queen takes row 10, column 2; slate has one square left, so its queen takes row 5, column 3; khaki has one square left, so its queen takes row 8, column 12; teal has one square left, so its queen takes row 11, column 6; orange has one square left, so its queen takes row 9, 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 9, column 10.
The board after step 15 — 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 #205
Puzzle #205 is one of the hard-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.
There is exactly one way to finish #205, 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 #205 are: indigo (1 square), rose (1 square), blue (4 squares), red (5 squares), pale yellow (10 squares), amber (11 squares), slate (13 squares), khaki (14 squares), sea green (17 squares), teal (21 squares), mint (23 squares), orange (24 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the orange region is the roomiest area on the grid with 24 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So indigo, with 1 square, is under far more pressure than orange with 24. A 23-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×1 frame; amber is the loosest, occupying only 46% of its 4×6 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Here is the full footprint of every color on puzzle #205, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 7–7). It never leaves row 1, so its queen is locked to that row.
Rose occupies 1 square within rows 12–12, columns 1–1. It never leaves row 12, so its queen is locked to that row.
Blue: 4 squares across rows 1–3, columns 11–12.
Red covers 5 squares, spanning 4 rows and 2 columns (rows 3–6, columns 4–5).
Pale yellow occupies 10 squares within rows 6–9, columns 5–8.
Amber: 11 squares across rows 1–4, columns 1–6.
Slate covers 13 squares, spanning 5 rows and 3 columns (rows 2–6, columns 1–3).
Khaki occupies 14 squares within rows 3–11, columns 10–12.
Sea green: 17 squares across rows 6–12, columns 1–5.
Teal covers 21 squares, spanning 5 rows and 6 columns (rows 8–12, columns 2–7).
Mint occupies 23 squares within rows 1–5, columns 6–11.
Orange: 24 squares across rows 5–12, columns 8–12.
Where to start on this board
Open on the tightest color. Here that is indigo, confined to 1 square between rows 1 and 1 and columns 7 and 7. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #205.
Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Rose 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 #205
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 7, 10, 11 and 12 are the narrowest, touched by only 4 colors. Column 9 is the tightest column, with 2 colors.
A line with few colors is a line close to resolving. Where only 4 colors appear, one of them owns the row outright and the others must fit into the remaining 11 rows. Row 6 is the crowded extreme at 6 colors — worth revisiting later, not now.
Working through the middle game
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
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.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #205 is rated hard
The rating reflects how much the board concedes up front. Puzzle #205 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 4 colors, and the gap between its largest and smallest regions is 23 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
Stuck on #205 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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #205, start hunting for it near column 9.
A non-spoiling distribution check: solved, #205 carries 3 queens on the perimeter against 9 queens inside, 1 of them cornered. 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 #205?
Puzzle #205 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 4 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #205 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #205, 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 #205?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.