12x12 Queens Puzzle #132
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #132
What follows is a complete solve of puzzle #132, 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 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: teal has one square left, so its queen takes row 11, column 1; orange has one square left, so its queen takes row 9, column 2; khaki has one square left, so its queen takes row 8, column 4; sea green has one square left, so its queen takes row 10, column 6. 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 10, column 6.
Step 2. Indigo is down to 6 candidates in rows 1 and 2, columns 8–12, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about indigo itself.
Step 3. The amber region has 3 squares left, spread across rows 2–4, columns 11 and 12. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
Step 4. 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: 6 squares in all.
The board after step 4 — 4 of 12 queens placed. Step 5. Amber is down to 2 candidates in rows 2 and 4, columns 11 and 12, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 6. Only row 5, column 11 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 11, the rest of the slate region and every square adjacent to it — diagonals included.
Step 7. The amber region is down to one open square, at row 2, column 12. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 12, the remaining amber squares, and the ring of neighbours around row 2, column 12.
The board after step 7 — 6 of 12 queens placed. Step 8. Only row 1, column 10 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 10, in indigo and in the ring around that square is now dead.
Step 9. 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: 1 square come off.
Step 10. Mint cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 1 square in all.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: rose has one square left, so its queen takes row 12, column 3; pale yellow has one square left, so its queen takes row 7, column 7; red has one square left, so its queen takes row 6, column 9; blue has one square left, so its queen takes row 3, column 8; mint has one square left, so its queen takes row 4, 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 4, column 5.
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 #132
This is puzzle number 132 in the 12x12 collection, rated easy. The grid holds 144 squares split between twelve colored regions, and a finished board carries twelve queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
As with every puzzle in this collection, #132 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 #132 are: teal (1 square), blue (3 squares), khaki (3 squares), amber (4 squares), slate (4 squares), orange (4 squares), indigo (6 squares), sea green (6 squares), red (15 squares), rose (19 squares), mint (32 squares), pale yellow (47 squares). An even split would hand every color 12 squares, so the teal region is running 11 squares under that average while the pale yellow region is the roomiest area on the grid with 47 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Teal is working with 1 square while pale yellow has 47 to spare, a gap of 46. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The blue region is the most compact color here, filling 100% of the 1×3 box that encloses it, while pale yellow is the most scattered at 44% of its 9×12 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 easy board.
Teal: 1 square across rows 11–11, columns 1–1. It never leaves row 11, so its queen is locked to that row.
Blue covers 3 squares, spanning 1 row and 3 columns (rows 3–3, columns 8–10). It never leaves row 3, so its queen is locked to that row.
Khaki occupies 3 squares within rows 8–9, columns 4–5.
Amber: 4 squares across rows 2–4, columns 11–12.
Slate covers 4 squares, spanning 3 rows and 2 columns (rows 3–5, columns 11–12).
Orange occupies 4 squares within rows 9–10, columns 1–2.
Indigo: 6 squares across rows 1–2, columns 8–12.
Sea green covers 6 squares, spanning 3 rows and 4 columns (rows 8–10, columns 5–8).
Red occupies 15 squares within rows 4–7, columns 7–10.
Rose: 19 squares across rows 9–12, columns 1–9.
Mint covers 32 squares, spanning 6 rows and 9 columns (rows 1–6, columns 1–9).
Pale yellow occupies 47 squares within rows 4–12, columns 1–12.
Where to start on this board
The most constrained color is where a solve should begin, and on #132 that is teal with 1 square. It reaches from row 11 to row 11 and from column 1 to column 1 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Because teal never leaves row 11, its queen must be in that row — and that instantly settles row 11 for everyone else. Sweep along it and X out every square that is not teal. 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. Blue, indigo, khaki and orange 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 #132
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 7 and 12 are the narrowest, touched by only 2 colors. Column 3 is the tightest column, with 3 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 11 rows. Row 9 is the crowded extreme at 5 colors — worth revisiting later, not now.
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.
Resist the plausible-looking queen. On #132 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 #132 is rated easy
The easy label comes out of four measurable things about #132: three of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 46. 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 easy board from the rest.
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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 1 on this board.
A non-spoiling distribution check: solved, #132 carries 4 queens on the perimeter against 8 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
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 #132?
Puzzle #132 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #132 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #132, 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 #132?
Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.