12x12 Queens Puzzle #111

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 14-step reasoning is written out below.

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Step-by-step solution for puzzle #111

What follows is a complete solve of puzzle #111, 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 shadow.

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

Show the full walkthrough (7 steps) — contains the solution

  1. Step 1. Only row 5, column 5 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 5, the rest of the slate region and every square adjacent to it — diagonals included.

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

  3. Step 3. 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: amber has one square left, so its queen takes row 2, column 6; teal has one square left, so its queen takes row 11, column 7; rose has one square left, so its queen takes row 12, column 12; indigo has one square left, so its queen takes row 1, column 11; blue has one square left, so its queen takes row 3, column 10; sea green has one square left, so its queen takes row 10, column 2; khaki has one square left, so its queen takes row 8, column 1; orange has one square left, so its queen takes row 9, column 4. 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 4.

  4. Step 4. Mint is down to 3 candidates in rows 4 and 6, columns 8 and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.

    Puzzle #111 after step 4: 9 of 12 queens placed
    The board after step 4 — 9 of 12 queens placed.

  5. Step 5. The pale yellow region is down to one open square, at row 7, column 9. Every colour holds exactly one queen, so that square is forced. Row 7 and column 9 are now spoken for, along with the squares touching that queen.

  6. Step 6. Only row 4, column 8 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 8, the rest of the mint region and every square adjacent to it — diagonals included.

  7. Step 7. The red region is down to one open square, at row 6, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 3, the remaining red squares, and the ring of neighbours around row 6, column 3.

    Puzzle #111 after step 7: 12 of 12 queens placed
    The board after step 7 — 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 #111

12x12 puzzle #111 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 #111 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 #111 are: slate (1 square), indigo (2 squares), rose (2 squares), teal (3 squares), khaki (4 squares), sea green (7 squares), amber (8 squares), blue (10 squares), orange (18 squares), mint (21 squares), red (29 squares), pale yellow (39 squares). An even split would hand every color 12 squares, so the slate region is running 11 squares under that average while the pale yellow region is the roomiest area on the grid with 39 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Slate is working with 1 square while pale yellow has 39 to spare, a gap of 38. Attack the cramped end and the roomy regions tend to resolve themselves.

Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×2 box that encloses it, while blue is the most scattered at 50% of its 5×4 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

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.

Slate: 1 square across rows 5–5, columns 5–5. It never leaves row 5, so its queen is locked to that row.

Indigo covers 2 squares, spanning 1 row and 2 columns (rows 1–1, columns 11–12). It never leaves row 1, so its queen is locked to that row.

Rose occupies 2 squares within rows 11–12, columns 12–12. It sits wholly inside column 12, so its queen must be in that column.

Teal: 3 squares across rows 11–12, columns 6–7.

Khaki covers 4 squares, spanning 3 rows and 2 columns (rows 8–10, columns 1–2).

Sea green occupies 7 squares within rows 10–12, columns 1–3.

Amber: 8 squares across rows 1–3, columns 3–7.

Blue covers 10 squares, spanning 5 rows and 4 columns (rows 1–5, columns 9–12).

Orange occupies 18 squares within rows 6–12, columns 3–7.

Mint: 21 squares across rows 1–6, columns 6–11.

Red covers 29 squares, spanning 8 rows and 5 columns (rows 1–8, columns 1–5).

Pale yellow occupies 39 squares within rows 5–12, columns 6–12.

Where to start on this board

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

Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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. Indigo, teal and rose 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 #111

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 4, 7 and 9 are the narrowest, touched by only 3 colors. Column 8 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 12 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 #111 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.

Keep alternating between two views of the board. In the region view you ask which of the twelve colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 12x12 board unwinds.

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 #111 is rated easy

Ratings track how generous the opening is. On #111 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 38-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.

Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.

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.

Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around column 8 on this board.

As a sanity check rather than a spoiler: the finished solution to #111 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 #111?

Puzzle #111 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 #111 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #111, 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 #111?

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