12x12 Queens Puzzle #185
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 27-step reasoning is written out below.
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Step-by-step solution for puzzle #185
What follows is a complete solve of puzzle #185, worked the way a person works it rather than the way a computer does. It runs to 27 deductions — 12 queen placements and 15 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 shadow, region confined to one line, pairing argument on columns, proof by contradiction, last square in a column.
Show the full walkthrough (19 steps) — contains the solution
Step 1. Only row 6, column 1 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 1, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. Indigo is down to 4 candidates in rows 1 and 2, columns 2–4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
Step 3. Orange cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 8 squares in all.
Step 4. 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: 9 squares come off.
Step 5. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 7 squares in all.
The board after step 5 — 1 of 12 queens placed. Step 6. Here is the pairing argument. The indigo, mint, and teal regions have no open squares outside columns 3–5 — 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: 13 squares come off in one stroke.
Step 7. Wherever blue ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Now a short proof by contradiction. Suppose the amber queen went to row 2, column 11. Follow the forced moves that would create and the teal region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 9. Only row 2, column 9 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 9, the rest of the amber region and every square adjacent to it — diagonals included.
Step 10. Wherever slate 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 10 — 2 of 12 queens placed. Step 11. Test row 4, column 6 for blue: 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 12. Now a short proof by contradiction. Suppose the blue queen went to row 4, column 7. Follow the forced moves that would create and the teal region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 13. Test row 4, column 8 for blue: place a queen there, run the forced consequences through, and the teal region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 14. The blue region is down to one open square, at row 3, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 6, the remaining blue squares, and the ring of neighbours around row 3, column 6.
The board after step 14 — 3 of 12 queens placed. Step 15. The slate region has 2 squares left, spread across rows 4 and 5, columns 8 and 10. 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 16. Now a short proof by contradiction. Suppose the mint queen went to row 5, column 3. Follow the forced moves that would create and the khaki region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 17. Test row 5, column 4 for mint: place a queen there, run the forced consequences through, and the khaki region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 18. Now a short proof by contradiction. Suppose the mint queen went to row 5, column 5. Follow the forced moves that would create and the khaki region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 19. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: column 5 is down to one square, putting a queen on row 11, column 5; orange has one square left, so its queen takes row 9, column 2; mint has one square left, so its queen takes row 4, column 4; indigo has one square left, so its queen takes row 1, column 3; slate has one square left, so its queen takes row 5, column 8; pale yellow has one square left, so its queen takes row 7, column 11; sea green has one square left, so its queen takes row 10, column 10; khaki has one square left, so its queen takes row 8, column 7; rose has one square left, so its queen takes row 12, column 12. 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 12, column 12.
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 #185
Puzzle #185 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 #185, 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 #185 are: red (1 square), indigo (6 squares), amber (8 squares), orange (8 squares), pale yellow (10 squares), teal (11 squares), slate (12 squares), blue (15 squares), rose (15 squares), mint (16 squares), sea green (17 squares), khaki (25 squares). An even split would hand every color 12 squares, so the red region is running 11 squares under that average while the khaki region is the roomiest area on the grid with 25 squares.
Every color takes one queen and one only, whatever its size — which is why the 24 square difference between red and khaki 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. Red is the densest region on this grid at 100% of a 1×1 frame; rose is the loosest, occupying only 47% of its 4×8 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 #185, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Red occupies 1 square within rows 6–6, columns 1–1. It never leaves row 6, so its queen is locked to that row.
Indigo: 6 squares across rows 1–2, columns 1–4.
Amber covers 8 squares, spanning 2 rows and 6 columns (rows 1–2, columns 7–12).
Orange occupies 8 squares within rows 7–12, columns 1–2.
Pale yellow: 10 squares across rows 2–7, columns 10–12.
Teal covers 11 squares, spanning 4 rows and 4 columns (rows 9–12, columns 2–5).
Slate occupies 12 squares within rows 2–5, columns 7–11.
Blue: 15 squares across rows 1–4, columns 3–8.
Rose covers 15 squares, spanning 4 rows and 8 columns (rows 9–12, columns 5–12).
Mint occupies 16 squares within rows 3–8, columns 1–5.
Sea green: 17 squares across rows 7–11, columns 8–12.
Khaki covers 25 squares, spanning 6 rows and 8 columns (rows 5–10, columns 3–10).
Where to start on this board
Open on the tightest color. Here that is red, confined to 1 square between rows 6 and 6 and columns 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #185.
Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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 and amber 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 #185
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 12 are the narrowest, touched by only 3 colors. Column 6 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 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 11 rows. By contrast row 10 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
The middle of #185 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
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.
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 #185 is rated hard
The rating reflects how much the board concedes up front. Puzzle #185 has two regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 24 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.
Stuck on #185 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.
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 #185 is row 1.
As a sanity check rather than a spoiler: the finished solution to #185 puts 3 queens on the outer border and 9 queens in the interior, 1 of them in an actual 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 #185?
Puzzle #185 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #185 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #185, 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 #185?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.