12x12 Queens Puzzle #128

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 14-step reasoning is written out below.

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Step-by-step solution for puzzle #128

What follows is a complete solve of puzzle #128, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 12 queen placements and 2 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 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. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: orange has one square left, so its queen takes row 9, column 5; rose has one square left, so its queen takes row 12, column 2; indigo has one square left, so its queen takes row 1, column 1; amber has one square left, so its queen takes row 2, column 6; blue has one square left, so its queen takes row 3, column 12; sea green has one square left, so its queen takes row 10, column 3; teal has one square left, so its queen takes row 11, 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 11, column 7.

  2. Step 2. 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: 4 squares come off.

  3. Step 3. Only row 5, column 4 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 4, the rest of the slate region and every square adjacent to it — diagonals included.

    Puzzle #128 after step 3: 8 of 12 queens placed
    The board after step 3 — 8 of 12 queens placed.

  4. Step 4. All of the red region's remaining squares (2 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.

  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: pale yellow has one square left, so its queen takes row 7, column 8; mint has one square left, so its queen takes row 4, column 9; red has one square left, so its queen takes row 6, column 11; khaki has one square left, so its queen takes row 8, 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 8, column 10.

    Puzzle #128 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 #128

This is puzzle number 128 in the 12x12 collection, rated hard. 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 #128 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 #128 are: orange (1 square), rose (1 square), indigo (3 squares), amber (5 squares), blue (5 squares), red (10 squares), teal (10 squares), pale yellow (14 squares), mint (15 squares), sea green (20 squares), slate (28 squares), khaki (32 squares). An even split would hand every color 12 squares, so the orange region is running 11 squares under that average while the khaki 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 31 square difference between orange 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. Orange is the tidiest shape on #128, packing 100% of its 1×1 bounding box, whereas blue straggles across its 3×3 box at just 56%. 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.

Orange occupies 1 square within rows 9–9, columns 5–5. It never leaves row 9, so its queen is locked to that row.

Rose: 1 square across rows 12–12, columns 2–2. It never leaves row 12, so its queen is locked to that row.

Indigo covers 3 squares, spanning 2 rows and 2 columns (rows 1–2, columns 1–2).

Amber occupies 5 squares within rows 1–2, columns 5–7.

Blue: 5 squares across rows 1–3, columns 10–12.

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

Teal occupies 10 squares within rows 9–12, columns 4–7.

Pale yellow: 14 squares across rows 5–8, columns 4–8.

Mint covers 15 squares, spanning 4 rows and 5 columns (rows 1–4, columns 7–11).

Sea green occupies 20 squares within rows 6–12, columns 1–5.

Slate: 28 squares across rows 1–8, columns 1–6.

Khaki covers 32 squares, spanning 7 rows and 6 columns (rows 6–12, columns 7–12).

Where to start on this board

The most constrained color is where a solve should begin, and on #128 that is orange with 1 square. It reaches from row 9 to row 9 and from column 5 to column 5 — 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 orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. 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, indigo and amber 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 #128

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3, 4, 5, 10 and 11 are the narrowest, touched by only 3 colors. Column 3 is the tightest column, with 2 colors.

Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 11 rows. By contrast row 6 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.

Working through the middle game

The middle of #128 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.

With twelve queens to seat and twelve regions competing over 144 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 12x12 boards quickly and players who stall halfway.

Resist the plausible-looking queen. On #128 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.

Why puzzle #128 is rated hard

Ratings track how generous the opening is. On #128 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 31-square gap between the largest and smallest regions. Those four numbers largely explain the hard 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.

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.

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 #128 is column 3.

As a sanity check rather than a spoiler: the finished solution to #128 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

  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 #128?

Puzzle #128 is rated hard. 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 #128 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #128, 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 #128?

Start with the orange region — the most constrained color on this board, with 1 square spanning rows 9–9 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.