12x12 Queens Puzzle #165
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 #165
What follows is a complete solve of puzzle #165, 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 confined to one line, region shadow, pairing argument on rows, pairing argument on columns, proof by contradiction.
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. The rose region is down to one open square, at row 12, column 12. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 12 and column 12, the remaining rose squares, and the ring of neighbours around row 12, column 12.
Step 3. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 10 squares in all.
Step 4. Wherever amber ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Mint is down to 4 candidates in rows 2, 3, 4, and 7, columns 2 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about mint itself.
The board after step 5 — 2 of 12 queens placed. Step 6. The amber region has 4 squares left, spread across rows 2 and 3, columns 3, 5, and 6. 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 7. Wherever pale yellow 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.
Step 8. Blue is down to 6 candidates in rows 2 and 3, columns 7–11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 9. The sea green region has 6 squares left, spread across rows 8–11, columns 2–4. 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 10. 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: 7 squares come off.
The board after step 10 — 2 of 12 queens placed. Step 11. Sea green is down to 3 candidates in rows 8–10, columns 2–4, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about sea green itself.
Step 12. 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: 4 squares come off in one stroke.
Step 13. Wherever mint ends up among its 2 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 14. Here is the pairing argument. The indigo and pale yellow regions have no open squares outside columns 10 and 11 — 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: 11 squares come off in one stroke.
The board after step 14 — 2 of 12 queens placed. Step 15. Only row 11, column 6 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 6, in teal and in the ring around that square is now dead.
Step 16. Here is the pairing argument. The blue, slate, and orange regions have no open squares outside columns 7–9 — 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: 3 squares come off in one stroke.
Step 17. Test row 2, column 5 for amber: place a queen there, run the forced consequences through, and row 8 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 18. Now a short proof by contradiction. Suppose the amber queen went to row 3, column 5. Follow the forced moves that would create and the pale yellow 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: amber has one square left, so its queen takes row 2, column 3; blue has one square left, so its queen takes row 3, column 9; mint has one square left, so its queen takes row 4, column 2; 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; indigo has one square left, so its queen takes row 1, column 10; orange has one square left, so its queen takes row 9, column 7; sea green has one square left, so its queen takes row 10, column 4; khaki has one square left, so its queen takes row 8, column 5. 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 8, column 5.
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 #165
Puzzle #165 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.
Like every board on this site, #165 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #165 are: red (1 square), rose (1 square), indigo (3 squares), mint (10 squares), teal (10 squares), blue (12 squares), amber (13 squares), pale yellow (14 squares), slate (15 squares), sea green (16 squares), orange (18 squares), khaki (31 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 31 squares.
Every color takes one queen and one only, whatever its size — which is why the 30 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. Indigo is the densest region on this grid at 100% of a 1×3 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
Here is the full footprint of every color on puzzle #165, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Red: 1 square across rows 6–6, columns 1–1. It never leaves row 6, so its queen is locked to that row.
Rose covers 1 square, spanning 1 row and 1 column (rows 12–12, columns 12–12). It never leaves row 12, so its queen is locked to that row.
Indigo occupies 3 squares within rows 1–1, columns 10–12. It never leaves row 1, so its queen is locked to that row.
Mint: 10 squares across rows 2–7, columns 1–3.
Teal covers 10 squares, spanning 2 rows and 7 columns (rows 11–12, columns 5–11).
Blue occupies 12 squares within rows 1–4, columns 6–11.
Amber: 13 squares across rows 1–3, columns 1–7.
Pale yellow covers 14 squares, spanning 10 rows and 3 columns (rows 2–11, columns 10–12).
Slate occupies 15 squares within rows 3–9, columns 6–10.
Sea green: 16 squares across rows 7–12, columns 1–4.
Orange covers 18 squares, spanning 5 rows and 6 columns (rows 7–11, columns 6–11).
Khaki occupies 31 squares within rows 2–11, columns 2–8.
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 #165.
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, rose 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 #165
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. Columns 4, 5 and 12 are the tightest columns, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 11 rows. Row 7 sits at the far end with 6 colors crossing it; it will almost certainly be among the last to settle.
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.
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 #165 is rated hard
The rating reflects how much the board concedes up front. Puzzle #165 has five 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 30 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
If #165 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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 #165 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 #165?
Puzzle #165 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #165 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #165, 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 #165?
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.