12x12 Queens Puzzle #139

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 18-step reasoning is written out below.

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Step-by-step solution for puzzle #139

What follows is a complete solve of puzzle #139, 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 pairing argument on rows.

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

Show the full walkthrough (8 steps) — contains the solution

  1. Step 1. Slate cannot leave column 9 — every one of its open squares (2 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 14 squares in all.

  2. Step 2. Teal is down to 7 candidates in rows 11 and 12, columns 2–7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about teal itself.

  3. Step 3. 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 10; teal has one square left, so its queen takes row 11, column 7; sea green has one square left, so its queen takes row 10, column 1; orange has one square left, so its queen takes row 9, column 12. 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 9, column 12.

  4. Step 4. Khaki cannot leave column 4 — every one of its open squares (2 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 10 squares in all.

    Puzzle #139 after step 4: 4 of 12 queens placed
    The board after step 4 — 4 of 12 queens placed.

  5. Step 5. Red is down to 4 candidates in rows 6–8, columns 2 and 3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.

  6. Step 6. The blue region has 4 squares left, spread across rows 3–5, columns 2 and 3. 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. Here is the pairing argument. The red, pale yellow, and khaki regions have no open squares outside rows 6–8 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 6 squares come off in one stroke.

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

    Puzzle #139 after step 8: 12 of 12 queens placed
    The board after step 8 — 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 #139

12x12 puzzle #139 is rated easy. Twelve colored regions cover its 144 squares, and your job is to seat twelve queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.

Puzzle #139 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 #139 are: slate (2 squares), sea green (4 squares), rose (5 squares), teal (7 squares), blue (8 squares), orange (9 squares), red (11 squares), khaki (16 squares), mint (18 squares), pale yellow (18 squares), indigo (20 squares), amber (26 squares). An even split would hand every color 12 squares, so the slate region is running 10 squares under that average while the amber region is the roomiest area on the grid with 26 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Slate has only 2 places to put its queen; amber has 26. The spread between them on this board is 24 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

A region's outline can constrain it more than its size does. Here slate is the most solid, filling 100% of its 2×1 box, and khaki the most diffuse at 53% of its 5×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

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.

Slate covers 2 squares, spanning 2 rows and 1 column (rows 5–6, columns 9–9). It sits wholly inside column 9, so its queen must be in that column.

Sea green occupies 4 squares within rows 10–12, columns 1–2.

Rose: 5 squares across rows 10–12, columns 8–10.

Teal covers 7 squares, spanning 2 rows and 6 columns (rows 11–12, columns 2–7).

Blue occupies 8 squares within rows 3–5, columns 1–4.

Orange: 9 squares across rows 9–12, columns 10–12.

Red covers 11 squares, spanning 4 rows and 3 columns (rows 6–9, columns 1–3).

Khaki occupies 16 squares within rows 7–11, columns 2–7.

Mint: 18 squares across rows 4–9, columns 4–8.

Pale yellow covers 18 squares, spanning 6 rows and 5 columns (rows 6–11, columns 8–12).

Indigo occupies 20 squares within rows 1–4, columns 1–8.

Amber: 26 squares across rows 1–5, columns 7–12.

Where to start on this board

Begin where the choices are fewest. On this board that means slate, which owns just 2 squares inside a 2×1 window running from row 5 to row 6 and column 9 to column 9. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Because slate stays inside column 9, its queen belongs to that column and no other region may use it. Cross out the rest of column 9 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.

Work outward to the other flat regions next. Teal 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 #139

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 11 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 6 colors — worth revisiting later, not now.

Working through the middle game

The middle of #139 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.

Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.

Why puzzle #139 is rated easy

The easy label comes out of four measurable things about #139: one of its regions is locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 2 colors, and its largest and smallest regions differ by 24. 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.

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.

One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #139 the place to look for one is around row 1.

A non-spoiling distribution check: solved, #139 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

  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 #139?

Puzzle #139 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.

Does 12x12 puzzle #139 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #139, 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 #139?

Start with the slate region — the most constrained color on this board, with 2 squares spanning rows 5–6 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.