12x12 Queens Puzzle #163
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #163
What follows is a complete solve of puzzle #163, 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 region shadow.
Techniques this board needs: last square in a region, region shadow, region confined to one line.
Show the full walkthrough (11 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: slate has one square left, so its queen takes row 5, column 2; mint has one square left, so its queen takes row 4, column 12; sea green has one square left, so its queen takes row 10, column 11; rose has one square left, so its queen takes row 12, column 10; indigo has one square left, so its queen takes row 1, column 9. 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 1, column 9.
Step 2. The red region has 3 squares left, spread across rows 6 and 7, columns 7 and 8. 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 3. Wherever khaki 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 4. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
The board after step 4 — 5 of 12 queens placed. Step 5. The pale yellow region has 4 squares left, spread across rows 7, 8, and 11, columns 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 6. All of the teal region's remaining squares (5 open squares) lie in row 11. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
Step 7. Pale yellow is down to 3 candidates in rows 7 and 8, columns 5 and 6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about pale yellow itself.
The board after step 7 — 5 of 12 queens placed. Step 8. All of the red region's remaining squares (2 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 9. Only row 9, column 7 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 7, the rest of the orange region and every square adjacent to it — diagonals included.
Step 10. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: red has one square left, so its queen takes row 6, column 8; blue has one square left, so its queen takes row 3, column 3; khaki has one square left, so its queen takes row 8, column 4; pale yellow has one square left, so its queen takes row 7, column 6; teal has one square left, so its queen takes row 11, column 5; amber has one square left, so its queen takes row 2, column 1. 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 2, column 1.
The board after step 11 — 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 #163
12x12 puzzle #163 is rated easy. Twelve colored regions cover its 144 squares, and your job is to seat twelve queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Like every board on this site, #163 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 #163 are: slate (1 square), mint (3 squares), orange (3 squares), sea green (4 squares), rose (6 squares), pale yellow (11 squares), indigo (14 squares), amber (15 squares), khaki (15 squares), teal (19 squares), red (20 squares), blue (33 squares). An even split would hand every color 12 squares, so the slate region is running 11 squares under that average while the blue region is the roomiest area on the grid with 33 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Slate has only 1 place to put its queen; blue has 33. The spread between them on this board is 32 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here slate is the most solid, filling 100% of its 1×1 box, and khaki the most diffuse at 43% of its 7×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #163 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Slate covers 1 square, spanning 1 row and 1 column (rows 5–5, columns 2–2). It never leaves row 5, so its queen is locked to that row.
Mint occupies 3 squares within rows 4–5, columns 11–12.
Orange: 3 squares across rows 9–10, columns 7–8.
Sea green covers 4 squares, spanning 3 rows and 2 columns (rows 8–10, columns 11–12).
Rose occupies 6 squares within rows 11–12, columns 10–12.
Pale yellow: 11 squares across rows 7–11, columns 4–8.
Indigo covers 14 squares, spanning 5 rows and 4 columns (rows 1–5, columns 9–12).
Amber occupies 15 squares within rows 1–3, columns 1–6.
Khaki: 15 squares across rows 6–12, columns 1–5.
Teal covers 19 squares, spanning 4 rows and 8 columns (rows 9–12, columns 3–10).
Red occupies 20 squares within rows 5–9, columns 7–12.
Blue: 33 squares across rows 1–8, columns 1–9.
Where to start on this board
Begin where the choices are fewest. On this board that means slate, which owns just 1 square inside a 1×1 window running from row 5 to row 5 and column 2 to column 2. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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. Mint, orange and rose 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 #163
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 4, 6 and 12 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, 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 9 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.
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.
Resist the plausible-looking queen. On #163 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #163 is rated easy
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 32. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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 #163 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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #163 the place to look for one is around row 1.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 8 queens in the middle, and nothing in the corners. 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 #163?
Puzzle #163 is rated easy. 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 #163 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #163, 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 #163?
Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 2–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.