12x12 Queens Puzzle #220
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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #220
What follows is a complete solve of puzzle #220, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 12 queen placements and 9 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 line confined to one region.
Techniques this board needs: last square in a region, region shadow, region confined to one line, line confined to one region, last square in a column.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 8, column 7 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 7, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 2. Mint is down to 6 candidates in rows 3–5, columns 5, 6, 8, and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 3. The red region has 5 squares left, spread across rows 5–7, columns 5, 6, and 8. 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 teal ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 5. Rose cannot leave row 12 — every one of its open squares (3 open squares) sits there. That row belongs to rose, so every square on it owned by another colour is dead: 8 squares in all.
The board after step 5 — 1 of 12 queens placed. Step 6. The teal region is down to one open square, at row 11, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 10, the remaining teal squares, and the ring of neighbours around row 11, column 10.
Step 7. Only row 10, column 8 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 8, in sea green and in the ring around that square is now dead.
Step 8. Amber is down to 2 candidates in rows 2 and 3, columns 9 and 11, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 9. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 10 squares in all.
The board after step 9 — 3 of 12 queens placed. Step 10. Wherever red ends up among its 2 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 11. Orange cannot leave row 9 — every one of its open squares (2 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 5 squares in all.
Step 12. 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: pale yellow has one square left, so its queen takes row 7, column 1; red has one square left, so its queen takes row 6, column 6; mint has one square left, so its queen takes row 4, column 5; slate has one square left, so its queen takes row 5, column 2; rose has one square left, so its queen takes row 12, column 3. 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 3.
Step 13. Column 4 has only indigo squares left (2 open squares). The column needs a queen and only indigo can provide one, which pins that colour to this column and kills its squares elsewhere: 1 square.
Step 14. 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: column 9 is down to one square, putting a queen on row 2, column 9; indigo has one square left, so its queen takes row 1, column 4; blue has one square left, so its queen takes row 3, column 12; orange has one square left, so its queen takes row 9, column 11. 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 9, column 11.
The board after step 14 — 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 #220
This is puzzle number 220 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.
Puzzle #220 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 #220 are: khaki (1 square), rose (3 squares), teal (4 squares), red (8 squares), amber (9 squares), mint (9 squares), pale yellow (11 squares), sea green (16 squares), slate (18 squares), blue (19 squares), orange (21 squares), indigo (25 squares). An even split would hand every color 12 squares, so the khaki region is running 11 squares under that average while the indigo region is the roomiest area on the grid with 25 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Khaki is working with 1 square while indigo has 25 to spare, a gap of 24. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The khaki region is the most compact color here, filling 100% of the 1×1 box that encloses it, while amber is the most scattered at 45% of its 4×5 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
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Khaki covers 1 square, spanning 1 row and 1 column (rows 8–8, columns 7–7). It never leaves row 8, so its queen is locked to that row.
Rose occupies 3 squares within rows 12–12, columns 1–3. It never leaves row 12, so its queen is locked to that row.
Teal: 4 squares across rows 11–12, columns 10–12.
Red covers 8 squares, spanning 3 rows and 4 columns (rows 5–7, columns 5–8).
Amber occupies 9 squares within rows 1–4, columns 7–11.
Mint: 9 squares across rows 3–5, columns 5–9.
Pale yellow covers 11 squares, spanning 4 rows and 5 columns (rows 7–10, columns 1–5).
Sea green occupies 16 squares within rows 10–12, columns 1–9.
Slate: 18 squares across rows 4–9, columns 1–6.
Blue covers 19 squares, spanning 7 rows and 4 columns (rows 1–7, columns 9–12).
Orange occupies 21 squares within rows 7–11, columns 6–12.
Indigo: 25 squares across rows 1–5, columns 1–9.
Where to start on this board
The most constrained color is where a solve should begin, and on #220 that is khaki with 1 square. It reaches from row 8 to row 8 and from column 7 to column 7 — 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 khaki never leaves row 8, its queen must be in that row — and that instantly settles row 8 for everyone else. Sweep along it and X out every square that is not khaki. 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 teal 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 #220
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 6, 9, 10, 11 and 12 are the narrowest, touched by only 3 colors. Column 12 is the tightest column, with 3 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 7, meeting 5 colors, is the opposite case — the busiest line on #220 and the last one you should expect to crack.
Working through the middle game
The middle of #220 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
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 #220 is rated easy
Ratings track how generous the opening is. On #220 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 24-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
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.
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.
Here is a shape check that gives nothing away: when #220 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 #220?
Puzzle #220 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #220 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #220, 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 #220?
Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.