12x12 Queens Puzzle #30
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #30
What follows is a complete solve of puzzle #30, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 12 queen placements and 6 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. 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. Only row 8, column 2 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 2, in khaki and in the ring around that square is now dead.
Step 4. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.
The board after step 4 — 3 of 12 queens placed. Step 5. Blue cannot leave row 3 — every one of its open squares (3 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 4 squares in all.
Step 6. The mint region is down to one open square, at row 4, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 11, the remaining mint squares, and the ring of neighbours around row 4, column 11.
Step 7. Only row 5, column 6 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 6, in slate and in the ring around that square is now dead.
Step 8. Red is down to 2 candidates in rows 6 and 7, columns 8 and 10, and they overlap enough to cover 5 squares elsewhere. Cross those out without deciding anything about red itself.
The board after step 8 — 5 of 12 queens placed. Step 9. Teal cannot leave row 11 — every one of its open squares (2 open squares) sits there. That row belongs to teal, so every square on it owned by another colour is dead: 7 squares in all.
Step 10. All of the sea green region's remaining squares (3 open squares) lie in row 10. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
Step 11. Orange cannot leave row 9 — every one of its open squares (3 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 2 squares in all.
Step 12. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: column 5 is down to one square, putting a queen on row 7, column 5; red has one square left, so its queen takes row 6, column 8; amber has one square left, so its queen takes row 2, column 9; sea green has one square left, so its queen takes row 10, column 7; blue has one square left, so its queen takes row 3, column 3; orange has one square left, so its queen takes row 9, column 10; teal has one square left, so its queen takes row 11, column 4. 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 11, column 4.
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 #30
Board #30 of the 12x12 bank carries a hard rating. Its 144 squares are shared between twelve colored regions, and the solution places twelve queens: one per row, one per column, one per region, none of them side by side or corner to corner.
As with every puzzle in this collection, #30 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 #30 are: indigo (1 square), rose (1 square), amber (5 squares), khaki (6 squares), teal (8 squares), slate (9 squares), mint (12 squares), red (17 squares), sea green (17 squares), pale yellow (20 squares), blue (24 squares), orange (24 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the orange region is the roomiest area on the grid with 24 squares.
Every color takes one queen and one only, whatever its size — which is why the 23 square difference between indigo and orange 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.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×1 box that encloses it, while red is the most scattered at 40% of its 6×7 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
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 hard board.
Indigo: 1 square across rows 1–1, columns 12–12. It never leaves row 1, so its queen is locked to that row.
Rose covers 1 square, spanning 1 row and 1 column (rows 12–12, columns 1–1). It never leaves row 12, so its queen is locked to that row.
Amber occupies 5 squares within rows 1–2, columns 8–10.
Khaki: 6 squares across rows 5–9, columns 1–2.
Teal covers 8 squares, spanning 3 rows and 4 columns (rows 10–12, columns 1–4).
Slate occupies 9 squares within rows 3–5, columns 3–8.
Mint: 12 squares across rows 1–5, columns 8–12.
Red covers 17 squares, spanning 6 rows and 7 columns (rows 4–9, columns 6–12).
Sea green occupies 17 squares within rows 10–12, columns 4–11.
Pale yellow: 20 squares across rows 5–10, columns 2–6.
Blue covers 24 squares, spanning 7 rows and 7 columns (rows 1–7, columns 1–7).
Orange occupies 24 squares within rows 6–12, columns 7–12.
Where to start on this board
Indigo is the natural opening on #30: it is the smallest region on the grid at 1 square, boxed into rows 1–1 and columns 12–12. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
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 amber 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 #30
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 3 and 11 are the narrowest, touched by only 3 colors. Columns 1, 2, 3, 5, 11 and 12 are the tightest columns, with 4 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 5 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
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
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 #30 is rated hard
The hard label comes out of four measurable things about #30: 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 23. Boards that score tight on those measures give up their first queen fast.
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.
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 #30 is row 2.
Use this as a rough check on your progress: the completed board has 2 queens around the border and 10 queens in the middle, including 2 in 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 #30?
Puzzle #30 is rated hard. 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 #30 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #30, 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 #30?
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.