12x12 Queens Puzzle #216
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #216
What follows is a complete solve of puzzle #216, 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 line confined to one region.
Techniques this board needs: last square in a region, region confined to one line, region shadow, line confined to one region, last square in a row.
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: indigo has one square left, so its queen takes row 1, column 12; blue has one square left, so its queen takes row 3, column 11; rose has one square left, so its queen takes row 12, column 2; khaki has one square left, so its queen takes row 8, 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 8, column 3.
Step 2. Mint cannot leave column 1 — every one of its open squares (4 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 3 squares in all.
Step 3. The red region has 3 squares left, spread across rows 5 and 6, columns 4 and 5. 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. Wherever orange ends up among its 2 squares, the same squares fall within reach of it — 4 squares in total, impossible regardless of how the colour resolves.
The board after step 4 — 4 of 12 queens placed. Step 5. All of the sea green region's remaining squares (2 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 8 squares come off.
Step 6. Only row 6, column 4 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 4, the rest of the red region and every square adjacent to it — diagonals included.
Step 7. The amber region is down to one open square, at row 2, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 6, the remaining amber squares, and the ring of neighbours around row 2, column 6.
The board after step 7 — 6 of 12 queens placed. Step 8. Slate is down to 3 candidates in rows 4 and 5, columns 8–10, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about slate itself.
Step 9. The pale yellow region has 3 squares left, spread across rows 4, 5, and 7, columns 7 and 8. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 10. Row 11 has only teal squares left (4 open squares). The row needs a queen and only teal can provide one, which pins that colour to this row and kills its squares elsewhere: 5 squares.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: row 10 is down to one square, putting a queen on row 10, column 5; row 9 is down to one square, putting a queen on row 9, column 9; slate has one square left, so its queen takes row 5, column 10; mint has one square left, so its queen takes row 4, column 1; pale yellow has one square left, so its queen takes row 7, column 8; teal has one square left, so its queen takes row 11, 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 11, column 7.
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 #216
This is puzzle number 216 in the 12x12 collection, rated hard. 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 #216 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 #216 are: indigo (1 square), rose (1 square), sea green (4 squares), orange (5 squares), blue (6 squares), khaki (7 squares), pale yellow (11 squares), amber (14 squares), red (16 squares), mint (17 squares), teal (30 squares), slate (32 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the slate region is the roomiest area on the grid with 32 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Indigo is working with 1 square while slate has 32 to spare, a gap of 31. Attack the cramped end and the roomy regions tend to resolve themselves.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #216, packing 100% of its 1×1 bounding box, whereas slate straggles across its 12×6 box at just 44%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #216, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
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 2–2). It never leaves row 12, so its queen is locked to that row.
Sea green occupies 4 squares within rows 7–10, columns 5–5. It sits wholly inside column 5, so its queen must be in that column.
Orange: 5 squares across rows 7–9, columns 9–11.
Blue covers 6 squares, spanning 4 rows and 2 columns (rows 2–5, columns 11–12).
Khaki occupies 7 squares within rows 8–12, columns 1–3.
Pale yellow: 11 squares across rows 4–8, columns 6–9.
Amber covers 14 squares, spanning 5 rows and 5 columns (rows 1–5, columns 4–8).
Red occupies 16 squares within rows 5–10, columns 1–5.
Mint: 17 squares across rows 1–6, columns 1–4.
Teal covers 30 squares, spanning 7 rows and 9 columns (rows 6–12, columns 3–11).
Slate occupies 32 squares within rows 1–12, columns 7–12.
Where to start on this board
The most constrained color is where a solve should begin, and on #216 that is indigo with 1 square. It reaches from row 1 to row 1 and from column 12 to column 12 — 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 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 is no more than two rows tall, so its queen is 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 #216
A quick way to find the next move is to count how many different colors touch each line. On this board, row 11 is the narrowest, touched by only 3 colors. Columns 1, 6, 10 and 12 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 11 rows. By contrast row 8 meets 7 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
Resist the plausible-looking queen. On #216 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 #216 is rated hard
The rating reflects how much the board concedes up front. Puzzle #216 has five regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 31 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
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 11 on this board.
As a sanity check rather than a spoiler: the finished solution to #216 puts 3 queens on the outer border and 9 queens in the interior, 1 of them in an actual corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #216?
Puzzle #216 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #216 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #216, 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 #216?
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.