12x12 Queens Puzzle #206
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 #206
What follows is a complete solve of puzzle #206, 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 line confined to one region.
Techniques this board needs: last square in a region, region shadow, line confined to one region, last square in a column, region confined to one line.
Show the full walkthrough (10 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 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 12 and column 3, the remaining rose squares, and the ring of neighbours around row 12, column 3.
Step 3. The blue region has 3 squares left, spread across rows 2 and 3, columns 9–11. 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.
The board after step 3 — 2 of 12 queens placed. Step 4. Wherever khaki 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. Sea green is down to 2 candidates in rows 10 and 11, columns 1 and 2, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about sea green itself.
Step 6. The teal region has 4 squares left, spread across rows 9–11, columns 9 and 10. 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 7. Column 5 has only slate squares left (10 open squares). The column needs a queen and only slate can provide one, which pins that colour to this column and kills its squares elsewhere: 19 squares.
The board after step 7 — 2 of 12 queens placed. Step 8. 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: column 6 is down to one square, putting a queen on row 2, column 6; blue has one square left, so its queen takes row 3, column 11; khaki has one square left, so its queen takes row 8, column 10; teal has one square left, so its queen takes row 11, column 9; sea green has one square left, so its queen takes row 10, column 2; mint has one square left, so its queen takes row 4, column 1. 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 1.
Step 9. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
Step 10. 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: pale yellow has one square left, so its queen takes row 7, column 4; slate has one square left, so its queen takes row 5, column 5; red has one square left, so its queen takes row 6, column 8; 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 10 — 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 #206
Board #206 of the 12x12 bank carries a medium 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, #206 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 #206 are: indigo (1 square), rose (1 square), sea green (7 squares), blue (9 squares), orange (9 squares), khaki (10 squares), teal (10 squares), amber (11 squares), mint (11 squares), pale yellow (17 squares), red (20 squares), slate (38 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 38 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 38 to spare, a gap of 37. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and teal the most diffuse at 50% of its 4×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Here is the full footprint of every color on puzzle #206, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo occupies 1 square within rows 1–1, columns 12–12. It never leaves row 1, so its queen is locked to that row.
Rose: 1 square across rows 12–12, columns 3–3. It never leaves row 12, so its queen is locked to that row.
Sea green covers 7 squares, spanning 3 rows and 3 columns (rows 10–12, columns 1–3).
Blue occupies 9 squares within rows 1–4, columns 9–12.
Orange: 9 squares across rows 8–11, columns 7–9.
Khaki covers 10 squares, spanning 6 rows and 3 columns (rows 7–12, columns 10–12).
Teal occupies 10 squares within rows 9–12, columns 7–11.
Amber: 11 squares across rows 1–4, columns 6–9.
Mint covers 11 squares, spanning 6 rows and 3 columns (rows 1–6, columns 1–3).
Pale yellow occupies 17 squares within rows 5–10, columns 1–4.
Red: 20 squares across rows 3–7, columns 7–12.
Slate covers 38 squares, spanning 12 rows and 6 columns (rows 1–12, columns 2–7).
Where to start on this board
Indigo is the natural opening on #206: 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 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 #206
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 5, 6, 7 and 8 are the narrowest, touched by only 4 colors. Column 5 is the tightest column, with 1 color.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 4 colors, then one of those regions has to own it, and every other region is competing for the remaining 11 rows. By contrast row 10 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
The whole middle game reduces to two sweeps. Sweep the twelve colors looking for one with a single square left; sweep the twelve rows and twelve columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 12x12 solve from a stalled one.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #206 is rated medium
The rating reflects how much the board concedes up front. Puzzle #206 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 4 colors, and the gap between its largest and smallest regions is 37 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.
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 column 5 on this board.
As a sanity check rather than a spoiler: the finished solution to #206 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 #206?
Puzzle #206 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 4 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #206 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #206, 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 #206?
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.