12x12 Queens Puzzle #69

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 18-step reasoning is written out below.

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Step-by-step solution for puzzle #69

What follows is a complete solve of puzzle #69, 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 region shadow.

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

Show the full walkthrough (11 steps) — contains the solution

  1. Step 1. 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.

  2. Step 2. All of the orange region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 11 squares come off.

  3. Step 3. Only row 7, column 2 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 2, in pale yellow and in the ring around that square is now dead.

  4. Step 4. Wherever sea green ends up among its 5 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.

    Puzzle #69 after step 4: 2 of 12 queens placed
    The board after step 4 — 2 of 12 queens placed.

  5. Step 5. 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: rose has one square left, so its queen takes row 12, column 3; sea green has one square left, so its queen takes row 10, column 4; orange has one square left, so its queen takes row 9, column 1; teal has one square left, so its queen takes row 11, 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 11, column 11.

  6. Step 6. The indigo region has 3 squares left, spread across rows 1 and 2, 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.

  7. Step 7. Wherever slate ends up among its 5 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.

    Puzzle #69 after step 7: 6 of 12 queens placed
    The board after step 7 — 6 of 12 queens placed.

  8. Step 8. Red cannot leave column 10 — 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: 4 squares in all.

  9. Step 9. The indigo region is down to one open square, at row 1, column 9. Every colour holds exactly one queen, so that square is forced. Row 1 and column 9 are now spoken for, along with the squares touching that queen.

  10. Step 10. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 1 square in all.

  11. Step 11. 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 8; slate has one square left, so its queen takes row 5, column 6; amber has one square left, so its queen takes row 2, column 5; khaki has one square left, so its queen takes row 8, column 7; red has one square left, so its queen takes row 6, column 10. 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 6, column 10.

    Puzzle #69 after step 11: 12 of 12 queens placed
    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 #69

Puzzle #69 is one of the hard-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 #69, 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 #69 are: blue (1 square), orange (2 squares), pale yellow (4 squares), indigo (8 squares), sea green (8 squares), rose (8 squares), teal (11 squares), red (12 squares), mint (15 squares), slate (16 squares), amber (17 squares), khaki (42 squares). An even split would hand every color 12 squares, so the blue region is running 11 squares under that average while the khaki region is the roomiest area on the grid with 42 squares.

Every color takes one queen and one only, whatever its size — which is why the 41 square difference between blue and khaki 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. Blue is the tidiest shape on #69, packing 100% of its 1×1 bounding box, whereas sea green straggles across its 6×3 box at just 44%. 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.

Blue: 1 square across rows 3–3, columns 12–12. It never leaves row 3, so its queen is locked to that row.

Orange covers 2 squares, spanning 2 rows and 1 column (rows 9–10, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.

Pale yellow occupies 4 squares within rows 6–8, columns 1–2.

Indigo: 8 squares across rows 1–3, columns 9–12.

Sea green covers 8 squares, spanning 6 rows and 3 columns (rows 7–12, columns 2–4).

Rose occupies 8 squares within rows 9–12, columns 1–3.

Teal: 11 squares across rows 8–12, columns 10–12.

Red covers 12 squares, spanning 6 rows and 3 columns (rows 4–9, columns 10–12).

Mint occupies 15 squares within rows 2–6, columns 7–11.

Slate: 16 squares across rows 3–6, columns 1–8.

Amber covers 17 squares, spanning 3 rows and 8 columns (rows 1–3, columns 1–8).

Khaki occupies 42 squares within rows 5–12, columns 3–10.

Where to start on this board

Open on the tightest color. Here that is blue, confined to 1 square between rows 3 and 3 and columns 12 and 12. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #69.

Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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. Orange 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 #69

A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Columns 5, 6 and 9 are the tightest columns, with 3 colors.

The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 11 rows. Row 9, meeting 6 colors, is the opposite case — the busiest line on #69 and the last one you should expect to crack.

Working through the middle game

Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.

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 #69 is rated hard

Ratings track how generous the opening is. On #69 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 41-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.

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 hard board from the rest.

Stuck on #69 despite the hard 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 #69 is row 1.

Here is a shape check that gives nothing away: when #69 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 #69?

Puzzle #69 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.

Does 12x12 puzzle #69 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #69, 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 #69?

Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 12–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.