12x12 Queens Puzzle #61
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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #61
What follows is a complete solve of puzzle #61, 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 region shadow.
Techniques this board needs: region shadow, last square in a region, region confined to one line.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Wherever indigo ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. Blue is down to 3 candidates in rows 3 and 4, columns 1 and 2, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 3. The mint region has 4 squares left, spread across rows 3–5, columns 3 and 4. 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 4. The slate region is down to one open square, at row 5, column 2. Every colour holds exactly one queen, so that square is forced. Row 5 and column 2 are now spoken for, along with the squares touching that queen.
Step 5. Only row 3, column 1 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 1, the rest of the blue region and every square adjacent to it — diagonals included.
The board after step 5 — 2 of 12 queens placed. Step 6. The mint region is down to one open square, at row 4, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 4, the remaining mint squares, and the ring of neighbours around row 4, column 4.
Step 7. Red cannot leave column 7 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 11 squares in all.
Step 8. All of the pale yellow region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 9. The khaki region has 5 squares left, spread across rows 6, 7, 8, 10, and 11, columns 5 and 6. 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 9 — 3 of 12 queens placed. Step 10. Wherever teal ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 11. Rose cannot leave row 12 — every one of its open squares (2 open squares) sits there. That row belongs to rose, so every square on it owned by another colour is dead: 8 squares in all.
Step 12. 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 3; red has one square left, so its queen takes row 6, column 7; teal has one square left, so its queen takes row 11, column 12; indigo has one square left, so its queen takes row 1, 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 1, column 11.
Step 13. Wherever khaki ends up among its 2 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
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: sea green has one square left, so its queen takes row 10, column 8; khaki has one square left, so its queen takes row 8, column 6; orange has one square left, so its queen takes row 9, column 10; rose has one square left, so its queen takes row 12, column 9; amber has one square left, so its queen takes row 2, 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 2, column 5.
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 #61
Puzzle #61 is one of the medium-rated boards in the 12x12 set. Twelve colors divide its 144 squares, and you win by placing twelve queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
Like every board on this site, #61 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #61 are: rose (2 squares), blue (3 squares), slate (3 squares), teal (4 squares), mint (5 squares), indigo (6 squares), red (11 squares), pale yellow (16 squares), khaki (16 squares), sea green (16 squares), amber (30 squares), orange (32 squares). An even split would hand every color 12 squares, so the rose region is running 10 squares under that average while the orange region is the roomiest area on the grid with 32 squares.
Every color takes one queen and one only, whatever its size — which is why the 30 square difference between rose and orange is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Square count is only half the story — how a color is arranged counts too. Slate is the tidiest shape on #61, packing 100% of its 1×3 bounding box, whereas sea green straggles across its 5×7 box at just 46%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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.
Rose covers 2 squares, spanning 1 row and 2 columns (rows 12–12, columns 8–9). It never leaves row 12, so its queen is locked to that row.
Blue occupies 3 squares within rows 3–4, columns 1–2.
Slate: 3 squares across rows 5–5, columns 1–3. It never leaves row 5, so its queen is locked to that row.
Teal covers 4 squares, spanning 2 rows and 3 columns (rows 11–12, columns 10–12).
Mint occupies 5 squares within rows 3–5, columns 2–4.
Indigo: 6 squares across rows 1–3, columns 10–12.
Red covers 11 squares, spanning 4 rows and 6 columns (rows 4–7, columns 6–11).
Pale yellow occupies 16 squares within rows 6–12, columns 1–3.
Khaki: 16 squares across rows 5–11, columns 3–6.
Sea green covers 16 squares, spanning 5 rows and 7 columns (rows 8–12, columns 2–8).
Amber occupies 30 squares within rows 1–4, columns 1–11.
Orange: 32 squares across rows 4–11, columns 7–12.
Where to start on this board
Open on the tightest color. Here that is rose, confined to 2 squares between rows 12 and 12 and columns 8 and 9. Its queen has nowhere else to go, which means those 1 row and 2 columns carry more constraint than anywhere else on #61.
Because rose never leaves row 12, its queen must be in that row — and that instantly settles row 12 for everyone else. Sweep along it and X out every square that is not rose. 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. Slate, blue 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 #61
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 2 are the narrowest, touched by only 2 colors. Columns 5 and 12 are the tightest columns, 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 11 is the crowded extreme at 5 colors — worth revisiting later, not now.
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.
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.
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 #61 is rated medium
Ratings track how generous the opening is. On #61 you get two regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 30-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
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.
If #61 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #61 is row 1.
A non-spoiling distribution check: solved, #61 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 #61?
Puzzle #61 is rated medium. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #61 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #61, 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 #61?
Start with the rose region — the most constrained color on this board, with 2 squares spanning rows 12–12 and columns 8–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.