12x12 Queens Puzzle #179
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #179
What follows is a complete solve of puzzle #179, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 12 queen placements and 4 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 confined to one line, region shadow, last square in a column.
Show the full walkthrough (12 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 12; amber has one square left, so its queen takes row 2, column 11; indigo has one square left, so its queen takes row 1, column 9; teal has one square left, so its queen takes row 11, column 4; pale yellow has one square left, so its queen takes row 7, 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 7, column 5.
Step 2. 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: 4 squares come off.
Step 3. Only row 4, column 1 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 1, in mint and in the ring around that square is now dead.
Step 4. All of the red region's remaining squares (2 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
The board after step 4 — 6 of 12 queens placed. Step 5. The khaki region has 4 squares left, spread across rows 8–10, columns 2 and 3. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 6. The rose region is down to one open square, at row 12, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 12 and column 2, the remaining rose squares, and the ring of neighbours around row 12, column 2.
Step 7. Only row 8, column 3 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 3, in khaki and in the ring around that square is now dead.
Step 8. 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. Row 3 and column 6 are now spoken for, along with the squares touching that queen.
The board after step 8 — 9 of 12 queens placed. Step 9. Sea green cannot leave row 10 — every one of its open squares (2 open squares) sits there. That row belongs to sea green, so every square on it owned by another colour is dead: 1 square in all.
Step 10. Column 7 now has exactly one open square, row 9, column 7, in the orange region. Columns must each hold a queen, so that placement is forced. That clears row 9, column 7, the rest of the orange region and every square adjacent to it — diagonals included.
Step 11. Only row 10, column 10 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 10, in sea green and in the ring around that square is now dead.
Step 12. The red region is down to one open square, at row 6, column 8. Every colour holds exactly one queen, so that square is forced. Row 6 and column 8 are now spoken for, along with the squares touching that queen.
The board after step 12 — 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 #179
12x12 puzzle #179 is rated hard. 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.
As with every puzzle in this collection, #179 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 #179 are: slate (1 square), teal (1 square), mint (4 squares), indigo (8 squares), amber (9 squares), pale yellow (9 squares), rose (9 squares), blue (17 squares), orange (19 squares), khaki (22 squares), sea green (22 squares), red (23 squares). An even split would hand every color 12 squares, so the slate region is running 11 squares under that average while the red region is the roomiest area on the grid with 23 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; red has 23. The spread between them on this board is 22 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 mint is the most solid, filling 100% of its 4×1 box, and orange the most diffuse at 45% of its 7×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #179 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 occupies 1 square within rows 5–5, columns 12–12. It never leaves row 5, so its queen is locked to that row.
Teal: 1 square across rows 11–11, columns 4–4. It never leaves row 11, so its queen is locked to that row.
Mint covers 4 squares, spanning 4 rows and 1 column (rows 2–5, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Indigo occupies 8 squares within rows 1–2, columns 6–11.
Amber: 9 squares across rows 1–6, columns 10–12.
Pale yellow covers 9 squares, spanning 6 rows and 3 columns (rows 7–12, columns 4–6).
Rose occupies 9 squares within rows 9–12, columns 1–4.
Blue: 17 squares across rows 1–4, columns 1–8.
Orange covers 19 squares, spanning 7 rows and 6 columns (rows 6–12, columns 5–10).
Khaki occupies 22 squares within rows 3–10, columns 1–5.
Sea green: 22 squares across rows 6–12, columns 8–12.
Red covers 23 squares, spanning 5 rows and 7 columns (rows 3–7, columns 5–11).
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 12 to column 12. 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. Teal and indigo 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 #179
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 3 colors. Columns 2, 3 and 12 are the tightest columns, 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 11 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
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.
Resist the plausible-looking queen. On #179 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 #179 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers five single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 22. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
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 #179 the place to look for one is around row 1.
As a sanity check rather than a spoiler: the finished solution to #179 puts 4 queens on the outer border and 8 queens in the interior, with none in a 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 #179?
Puzzle #179 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 #179 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #179, 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 #179?
Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 12–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.