12x12 Queens Puzzle #65

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 13-step reasoning is written out below.

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Step-by-step solution for puzzle #65

What follows is a complete solve of puzzle #65, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 12 queen placements and 1 elimination step 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 confined to one line.

Techniques this board needs: last square in a region, region confined to one line.

Show the full walkthrough (5 steps) — contains the solution

  1. Step 1. Only row 8, column 10 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 10, the rest of the khaki region and every square adjacent to it — diagonals included.

  2. Step 2. The teal region is down to one open square, at row 11, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 7, the remaining teal squares, and the ring of neighbours around row 11, column 7.

  3. Step 3. Only row 12, column 9 is still open in rose, and since each colour must take a queen, that settles it. Everything else in row 12, in column 9, in rose and in the ring around that square is now dead.

    Puzzle #65 after step 3: 3 of 12 queens placed
    The board after step 3 — 3 of 12 queens placed.

  4. Step 4. 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: 7 squares come off.

  5. Step 5. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: sea green has one square left, so its queen takes row 10, column 1; pale yellow has one square left, so its queen takes row 7, column 6; red has one square left, so its queen takes row 6, column 8; slate has one square left, so its queen takes row 5, column 2; orange has one square left, so its queen takes row 9, column 3; mint has one square left, so its queen takes row 4, column 4; blue has one square left, so its queen takes row 3, column 12; indigo has one square left, so its queen takes row 1, column 11; 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.

    Puzzle #65 after step 5: 12 of 12 queens placed
    The board after step 5 — 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 #65

Puzzle #65 is one of the easy-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.

There is exactly one way to finish #65, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these twelve regions is what sets the depth.

How the colors divide this board

From smallest to largest, the regions on puzzle #65 are: khaki (1 square), teal (1 square), orange (5 squares), slate (8 squares), sea green (9 squares), rose (10 squares), blue (11 squares), indigo (12 squares), amber (18 squares), mint (19 squares), pale yellow (20 squares), red (30 squares). An even split would hand every color 12 squares, so the khaki region is running 11 squares under that average while the red region is the roomiest area on the grid with 30 squares.

Every color takes one queen and one only, whatever its size — which is why the 29 square difference between khaki and red 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. Khaki is the tidiest shape on #65, packing 100% of its 1×1 bounding box, whereas mint straggles across its 6×7 box at just 45%. 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 #65, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Khaki occupies 1 square within rows 8–8, columns 10–10. It never leaves row 8, so its queen is locked to that row.

Teal: 1 square across rows 11–11, columns 7–7. It never leaves row 11, so its queen is locked to that row.

Orange covers 5 squares, spanning 2 rows and 3 columns (rows 8–9, columns 1–3).

Slate occupies 8 squares within rows 5–7, columns 1–4.

Sea green: 9 squares across rows 9–12, columns 1–3.

Rose covers 10 squares, spanning 3 rows and 6 columns (rows 10–12, columns 6–11).

Blue occupies 11 squares within rows 2–6, columns 10–12.

Indigo: 12 squares across rows 1–4, columns 8–12.

Amber covers 18 squares, spanning 5 rows and 6 columns (rows 1–5, columns 3–8).

Mint occupies 19 squares within rows 1–6, columns 1–7.

Pale yellow: 20 squares across rows 7–12, columns 3–7.

Red covers 30 squares, spanning 8 rows and 8 columns (rows 5–12, columns 5–12).

Where to start on this board

Open on the tightest color. Here that is khaki, confined to 1 square between rows 8 and 8 and columns 10 and 10. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #65.

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. Teal and orange 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 #65

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 7 are the narrowest, touched by only 3 colors. Columns 9 and 12 are the tightest columns, 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 11, meeting 5 colors, is the opposite case — the busiest line on #65 and the last one you should expect to crack.

Working through the middle game

The middle of #65 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.

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.

The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.

Why puzzle #65 is rated easy

The rating reflects how much the board concedes up front. Puzzle #65 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 29 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 easy board from the rest.

Stuck on #65 despite the easy rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.

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 #65 is row 1.

Here is a shape check that gives nothing away: when #65 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

  1. The board is an N×N grid divided into N colored regions.
  2. Place exactly one queen (♛) in each row, each column, and each colored region.
  3. No two queens may touch each other — not horizontally, vertically, or diagonally.
  4. 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.
  5. 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 #65?

Puzzle #65 is rated easy. 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 #65 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #65, 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 #65?

Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 10–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.