12x12 Queens Puzzle #208
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #208
What follows is a complete solve of puzzle #208, 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 proof by contradiction.
Techniques this board needs: last square in a region, region confined to one line, region shadow, line confined to one region, proof by contradiction.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 1, column 10 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 10, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The pale yellow region is down to one open square, at row 7, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 2, the remaining pale yellow squares, and the ring of neighbours around row 7, column 2.
Step 3. Blue cannot leave column 12 — 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: 9 squares in all.
Step 4. The khaki region is down to one open square, at row 8, column 11. Every colour holds exactly one queen, so that square is forced. Row 8 and column 11 are now spoken for, along with the squares touching that queen.
Step 5. Only row 12, column 9 is still open in rose, and since each colour must take a queen, that settles it. That clears row 12, column 9, the rest of the rose region and every square adjacent to it — diagonals included.
The board after step 5 — 4 of 12 queens placed. Step 6. The red region is down to one open square, at row 6, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 8, the remaining red squares, and the ring of neighbours around row 6, column 8.
Step 7. Teal cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to teal, so every square in it owned by another colour is dead: 5 squares in all.
Step 8. The amber region is down to one open square, at row 2, column 4. Every colour holds exactly one queen, so that square is forced. Row 2 and column 4 are now spoken for, along with the squares touching that queen.
Step 9. Only row 3, column 12 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 12, the rest of the blue region and every square adjacent to it — diagonals included.
The board after step 9 — 7 of 12 queens placed. Step 10. All of the mint region's remaining squares (2 open squares) lie in row 4. 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 is down to 4 candidates in rows 9–11, columns 5 and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about orange itself.
Step 12. Every open square left in row 5 (2 open squares) belongs to the slate region. Since that row must contain a queen, slate is the colour that supplies it — so slate squares anywhere else on the board are out, 2 squares in all.
Step 13. Test row 4, column 7 for mint: place a queen there, run the forced consequences through, and column 6 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 14. 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: mint has one square left, so its queen takes row 4, column 6; slate has one square left, so its queen takes row 5, column 3; sea green has one square left, so its queen takes row 10, column 5; 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 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 9, column 7.
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 #208
This is puzzle number 208 in the 12x12 collection, rated medium. 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 #208 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 #208 are: indigo (1 square), pale yellow (1 square), teal (5 squares), blue (8 squares), amber (9 squares), khaki (9 squares), rose (13 squares), red (16 squares), sea green (16 squares), orange (18 squares), mint (21 squares), slate (27 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 27 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 27 to spare, a gap of 26. Attack the cramped end and the roomy regions tend to resolve themselves.
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 sea green is the most scattered at 44% of its 6×6 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
Here is the full footprint of every color on puzzle #208, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 10–10). It never leaves row 1, so its queen is locked to that row.
Pale yellow occupies 1 square within rows 7–7, columns 2–2. It never leaves row 7, so its queen is locked to that row.
Teal: 5 squares across rows 9–12, columns 1–2.
Blue covers 8 squares, spanning 3 rows and 4 columns (rows 1–3, columns 9–12).
Amber occupies 9 squares within rows 1–3, columns 1–4.
Khaki: 9 squares across rows 4–8, columns 10–12.
Rose covers 13 squares, spanning 4 rows and 4 columns (rows 9–12, columns 9–12).
Red occupies 16 squares within rows 3–8, columns 8–11.
Sea green: 16 squares across rows 7–12, columns 1–6.
Orange covers 18 squares, spanning 6 rows and 6 columns (rows 7–12, columns 4–9).
Mint occupies 21 squares within rows 1–5, columns 4–9.
Slate: 27 squares across rows 2–9, columns 1–7.
Where to start on this board
The most constrained color is where a solve should begin, and on #208 that is indigo with 1 square. It reaches from row 1 to row 1 and from column 10 to column 10 — 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. Pale yellow 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 #208
A quick way to find the next move is to count how many different colors touch each line. On this board, row 6 is the narrowest, touched by only 3 colors. Columns 3, 7, 8 and 12 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 11 rows. Row 7 is the crowded extreme at 6 colors — worth revisiting later, not now.
Working through the middle game
The middle of #208 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 #208 is rated medium
The rating reflects how much the board concedes up front. Puzzle #208 has four 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 26 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
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 6 on this board.
A non-spoiling distribution check: solved, #208 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 #208?
Puzzle #208 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 #208 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #208, 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 #208?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 10–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.