12x12 Queens Puzzle #25
Difficulty: medium. 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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #25
What follows is a complete solve of puzzle #25, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 12 queen placements and 7 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, last square in a row.
Show the full walkthrough (16 steps) — contains the solution
Step 1. Only row 1, column 12 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 12, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The rose region is down to one open square, at row 12, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 12 and column 1, the remaining rose squares, and the ring of neighbours around row 12, column 1.
Step 3. The blue region has 5 squares left, spread across rows 3–5, columns 4–6. 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 4. Wherever mint ends up among its 3 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
Step 5. Blue is down to 3 candidates in rows 3 and 5, columns 4 and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
The board after step 5 — 2 of 12 queens placed. Step 6. All of the red region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 7. Only row 10, column 3 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 3, in sea green and in the ring around that square is now dead.
Step 8. The teal region is down to one open square, at row 11, column 11. Every colour holds exactly one queen, so that square is forced. Row 11 and column 11 are now spoken for, along with the squares touching that queen.
Step 9. Only row 9, column 9 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 9, the rest of the orange region and every square adjacent to it — diagonals included.
Step 10. All of the slate region's remaining squares (3 open squares) lie in column 4. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 11. Blue cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 4 squares in all.
The board after step 11 — 5 of 12 queens placed. Step 12. 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: khaki has one square left, so its queen takes row 8, column 6; mint has one square left, so its queen takes row 4, column 7; amber has one square left, so its queen takes row 2, column 8; row 7 is down to one square, putting a queen on row 7, column 10. 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 10.
Step 13. All of the slate region's remaining squares (2 open squares) lie in column 4. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.
Step 14. Only row 3, column 5 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 5, the rest of the blue region and every square adjacent to it — diagonals included.
Step 15. The red region is down to one open square, at row 6, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 2, the remaining red squares, and the ring of neighbours around row 6, column 2.
Step 16. Only row 5, column 4 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 4, in slate and in the ring around that square is now dead.
The board after step 16 — 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 #25
Puzzle #25 is one of the medium-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 #25, 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 #25 are: indigo (1 square), rose (1 square), mint (3 squares), blue (5 squares), orange (6 squares), red (7 squares), teal (11 squares), sea green (12 squares), amber (15 squares), khaki (17 squares), slate (20 squares), pale yellow (46 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the pale yellow region is the roomiest area on the grid with 46 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So indigo, with 1 square, is under far more pressure than pale yellow with 46. A 45-square gap like this one rewards players who start where the choices are fewest.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and orange the most diffuse at 50% of its 3×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a medium board.
Indigo covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 12–12). It never leaves row 1, so its queen is locked to that row.
Rose occupies 1 square within rows 12–12, columns 1–1. It never leaves row 12, so its queen is locked to that row.
Mint: 3 squares across rows 4–5, columns 6–7.
Blue covers 5 squares, spanning 3 rows and 3 columns (rows 3–5, columns 4–6).
Orange occupies 6 squares within rows 9–11, columns 7–10.
Red: 7 squares across rows 3–7, columns 1–2.
Teal covers 11 squares, spanning 3 rows and 6 columns (rows 10–12, columns 7–12).
Sea green occupies 12 squares within rows 7–12, columns 1–3.
Amber: 15 squares across rows 1–5, columns 5–9.
Khaki covers 17 squares, spanning 7 rows and 4 columns (rows 6–12, columns 3–6).
Slate occupies 20 squares within rows 1–8, columns 1–5.
Pale yellow: 46 squares across rows 1–12, columns 6–12.
Where to start on this board
Open on the tightest color. Here that is indigo, confined to 1 square between rows 1 and 1 and columns 12 and 12. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #25.
Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Rose and mint 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 #25
A quick way to find the next move is to count how many different colors touch each line. On this board, row 2 is the narrowest, touched by only 3 colors. Column 11 is the tightest column, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 11 rows. Row 5, meeting 6 colors, is the opposite case — the busiest line on #25 and the last one you should expect to crack.
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 #25 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 #25 is rated medium
The medium label comes out of four measurable things about #25: four of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 45. Boards that score tight on those measures give up their first queen fast.
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 medium board from the rest.
Stuck on #25 despite the medium 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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #25, start hunting for it near column 11.
Here is a shape check that gives nothing away: when #25 is solved, 2 queens sit on the outer edge of the grid and 10 sit inside it, with 2 queens 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 #25?
Puzzle #25 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #25 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #25, 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 #25?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 12–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.