12x12 Queens Puzzle #44

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 17-step reasoning is written out below.

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Step-by-step solution for puzzle #44

What follows is a complete solve of puzzle #44, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 12 queen placements and 5 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 pairing argument on columns.

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

Show the full walkthrough (6 steps) — contains the solution

  1. Step 1. Wherever amber 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.

  2. Step 2. 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: 14 squares come off.

  3. Step 3. The pale yellow region has 6 squares left, spread across rows 7–11, columns 1 and 2. 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.

    Puzzle #44 after step 3: 0 of 12 queens placed
    The board after step 3 — 0 of 12 queens placed.

  4. Step 4. All of the teal region's remaining squares (2 open squares) lie in column 6. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 13 squares come off.

  5. Step 5. Blue, red, and pale yellow are now boxed into columns 1–3 and nothing else. That is 3 colours needing 3 columns, so they fill those columns between them — which locks every remaining colour out and removes 16 squares at once.

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

    Puzzle #44 after step 6: 12 of 12 queens placed
    The board after step 6 — 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 #44

This is puzzle number 44 in the 12x12 collection, rated easy. 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.

There is exactly one way to finish #44, 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 #44 are: red (2 squares), teal (2 squares), amber (4 squares), khaki (4 squares), indigo (8 squares), blue (8 squares), pale yellow (8 squares), rose (11 squares), mint (15 squares), sea green (19 squares), orange (22 squares), slate (41 squares). An even split would hand every color 12 squares, so the red region is running 10 squares under that average while the slate region is the roomiest area on the grid with 41 squares.

Every color takes one queen and one only, whatever its size — which is why the 39 square difference between red and slate 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.

Shape matters as much as size. The red region is the most compact color here, filling 100% of the 1×2 box that encloses it, while sea green is the most scattered at 53% of its 6×6 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.

Region by region

Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a easy board.

Red occupies 2 squares within rows 6–6, columns 2–3. It never leaves row 6, so its queen is locked to that row.

Teal: 2 squares across rows 11–12, columns 6–6. It sits wholly inside column 6, so its queen must be in that column.

Amber covers 4 squares, spanning 2 rows and 3 columns (rows 1–2, columns 10–12).

Khaki occupies 4 squares within rows 7–9, columns 11–12.

Indigo: 8 squares across rows 1–3, columns 1–4.

Blue covers 8 squares, spanning 3 rows and 3 columns (rows 3–5, columns 1–3).

Pale yellow occupies 8 squares within rows 6–11, columns 1–2.

Rose: 11 squares across rows 9–12, columns 9–12.

Mint covers 15 squares, spanning 7 rows and 4 columns (rows 1–7, columns 9–12).

Sea green occupies 19 squares within rows 7–12, columns 5–10.

Orange: 22 squares across rows 7–12, columns 1–6.

Slate covers 41 squares, spanning 8 rows and 8 columns (rows 1–8, columns 4–11).

Where to start on this board

The most constrained color is where a solve should begin, and on #44 that is red with 2 squares. It reaches from row 6 to row 6 and from column 2 to column 3 — 1 row by 2 columns. 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 red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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. Amber 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 #44

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 4 and 5 are the narrowest, touched by only 3 colors. Columns 7 and 8 are the tightest columns, with 2 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 7, meeting 6 colors, is the opposite case — the busiest line on #44 and the last one you should expect to crack.

Working through the middle game

The middle of #44 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.

Two checks, run alternately, will carry you through the 144 squares of this grid. First: has any of the twelve regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 12x12 boards almost always run one of those checks and forget the other.

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 #44 is rated easy

The easy label comes out of four measurable things about #44: two of its regions are locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 3 colors, and its largest and smallest regions differ by 39. Boards that score tight on those measures give up their first queen fast.

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.

Stuck on #44 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 #44 is column 7.

Here is a shape check that gives nothing away: when #44 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 #44?

Puzzle #44 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.

Does 12x12 puzzle #44 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #44, 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 #44?

Start with the red region — the most constrained color on this board, with 2 squares spanning rows 6–6 and columns 2–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.