12x12 Queens Puzzle #79
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 24-step reasoning is written out below.
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Step-by-step solution for puzzle #79
What follows is a complete solve of puzzle #79, worked the way a person works it rather than the way a computer does. It runs to 24 deductions — 12 queen placements and 12 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, line confined to one region, last square in a row, last square in a column, proof by contradiction, region confined to one line.
Show the full walkthrough (21 steps) — contains the solution
Step 1. Only row 2, column 1 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 1, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. The red region is down to one open square, at row 6, column 12. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 12, the remaining red squares, and the ring of neighbours around row 6, column 12.
Step 3. Only row 1, column 11 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 11, in indigo and in the ring around that square is now dead.
Step 4. Wherever mint 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 5. Khaki is down to 3 candidates in rows 7 and 8, columns 9 and 10, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about khaki itself.
The board after step 5 — 3 of 12 queens placed. Step 6. The teal region has 4 squares left, spread across rows 10–12, 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 7. Row 3 has only blue squares left (8 open squares). The row needs a queen and only blue can provide one, which pins that colour to this row and kills its squares elsewhere: 15 squares.
Step 8. Row 4 has a single open square left, at column 10 in the mint region. Every row needs a queen, so this one is forced. Cross out the whole of row 4 and column 10, the remaining mint squares, and the ring of neighbours around row 4, column 10.
Step 9. Only row 8, column 9 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 9, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 10. Wherever pale yellow 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 11. Orange is down to 3 candidates in rows 9 and 10, columns 2 and 3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about orange itself.
The board after step 11 — 5 of 12 queens placed. Step 12. The teal region has 3 squares left, spread across rows 11 and 12, 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 13. Wherever rose 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 14. Every open square left in row 5 (2 open squares) belongs to the slate region. Since that row must contain a queen, slate is the colour that supplies it — so slate squares anywhere else on the board are out, 2 squares in all.
Step 15. Look along row 7: one square survives, row 7, column 5, which belongs to pale yellow. A row cannot be left empty, so the queen goes there. That clears row 7, column 5, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 16. Column 4 now has exactly one open square, row 3, column 4, in the blue region. Columns must each hold a queen, so that placement is forced. Everything else in row 3, in column 4, in blue and in the ring around that square is now dead.
The board after step 16 — 7 of 12 queens placed. Step 17. Sea green is down to 5 candidates in rows 9–11, columns 6–8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about sea green itself.
Step 18. Now a short proof by contradiction. Suppose the slate queen went to row 5, column 6. 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 19. Only row 5, column 8 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 8, in slate and in the ring around that square is now dead.
Step 20. All of the rose region's remaining squares (2 open squares) lie in row 12. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
Step 21. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: teal has one square left, so its queen takes row 11, column 3; orange has one square left, so its queen takes row 9, column 2; sea green has one square left, so its queen takes row 10, column 6; rose has one square left, so its queen takes row 12, column 7. 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 7.
The board after step 21 — 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 #79
12x12 puzzle #79 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.
Puzzle #79 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #79 are: amber (1 square), red (1 square), indigo (2 squares), teal (6 squares), pale yellow (10 squares), orange (10 squares), sea green (11 squares), khaki (12 squares), slate (14 squares), rose (16 squares), mint (17 squares), blue (44 squares). An even split would hand every color 12 squares, so the amber region is running 11 squares under that average while the blue region is the roomiest area on the grid with 44 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Amber has only 1 place to put its queen; blue has 44. The spread between them on this board is 43 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 indigo is the most solid, filling 100% of its 1×2 box, and sea green the most diffuse at 55% of its 4×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #79 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.
Amber covers 1 square, spanning 1 row and 1 column (rows 2–2, columns 1–1). It never leaves row 2, so its queen is locked to that row.
Red occupies 1 square within rows 6–6, columns 12–12. It never leaves row 6, so its queen is locked to that row.
Indigo: 2 squares across rows 1–1, columns 11–12. It never leaves row 1, so its queen is locked to that row.
Teal covers 6 squares, spanning 3 rows and 3 columns (rows 10–12, columns 1–3).
Pale yellow occupies 10 squares within rows 6–11, columns 4–6.
Orange: 10 squares across rows 7–11, columns 1–3.
Sea green covers 11 squares, spanning 4 rows and 5 columns (rows 9–12, columns 4–8).
Khaki occupies 12 squares within rows 7–11, columns 9–12.
Slate: 14 squares across rows 5–8, columns 6–11.
Rose covers 16 squares, spanning 4 rows and 7 columns (rows 9–12, columns 6–12).
Mint occupies 17 squares within rows 1–5, columns 8–12.
Blue: 44 squares across rows 1–7, columns 1–10.
Where to start on this board
Begin where the choices are fewest. On this board that means amber, which owns just 1 square inside a 1×1 window running from row 2 to row 2 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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 red 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 #79
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3 and 4 are the narrowest, touched by only 2 colors. Columns 2, 3, 4 and 5 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 11 rows. Row 11, meeting 6 colors, is the opposite case — the busiest line on #79 and the last one you should expect to crack.
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.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #79 is rated easy
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 2 colors, and a region-size spread of 43. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a easy board from the rest.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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 #79 the place to look for one is around row 3.
Here is a shape check that gives nothing away: when #79 is solved, 4 queens sit on the outer edge of the grid and 8 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #79?
Puzzle #79 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #79 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #79, 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 #79?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.