12x12 Queens Puzzle #263

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 19-step reasoning is written out below.

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Step-by-step solution for puzzle #263

What follows is a complete solve of puzzle #263, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 12 queen placements and 7 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, line confined to one region, last square in a column.

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

  1. Step 1. Wherever amber ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.

  2. Step 2. All of the red region's remaining squares (3 open squares) lie in row 6. 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. The teal region has 3 squares left, spread across rows 11 and 12, columns 1 and 2. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.

  4. Step 4. Here is the pairing argument. The amber and slate regions have no open squares outside columns 11 and 12 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 12 squares come off in one stroke.

    Puzzle #263 after step 4: 0 of 12 queens placed
    The board after step 4 — 0 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 10; teal has one square left, so its queen takes row 11, column 2; orange has one square left, so its queen takes row 9, column 1; red has one square left, so its queen takes row 6, column 3. 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 3.

  6. Step 6. Mint cannot leave column 9 — every one of its open squares (3 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 5 squares in all.

  7. Step 7. The sea green region is down to one open square, at row 10, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 8, the remaining sea green squares, and the ring of neighbours around row 10, column 8.

    Puzzle #263 after step 7: 5 of 12 queens placed
    The board after step 7 — 5 of 12 queens placed.

  8. Step 8. Only row 8, column 4 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 4, in khaki and in the ring around that square is now dead.

  9. Step 9. The indigo region has 4 squares left, spread across rows 1, 2, and 4, columns 6 and 7. 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.

  10. Step 10. Row 3 has only blue squares left (2 open squares). The row needs a queen and only blue can provide one, which pins that colour to this row and kills its squares elsewhere: 7 squares.

  11. Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: column 5 is down to one square, putting a queen on row 3, column 5; column 6 is down to one square, putting a queen on row 7, column 6; slate has one square left, so its queen takes row 5, column 12; amber has one square left, so its queen takes row 2, column 11; mint has one square left, so its queen takes row 4, column 9; indigo has one square left, so its queen takes row 1, 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 1, column 7.

    Puzzle #263 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 #263

12x12 puzzle #263 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.

There is exactly one way to finish #263, 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 #263 are: amber (3 squares), red (3 squares), teal (3 squares), slate (6 squares), rose (7 squares), orange (8 squares), indigo (12 squares), khaki (12 squares), mint (13 squares), pale yellow (19 squares), sea green (26 squares), blue (32 squares). An even split would hand every color 12 squares, so the amber region is running 9 squares under that average while the blue region is the roomiest area on the grid with 32 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Amber has only 3 places to put its queen; blue has 32. The spread between them on this board is 29 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 red is the most solid, filling 100% of its 1×3 box, and sea green the most diffuse at 46% of its 7×8 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

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.

Amber occupies 3 squares within rows 1–2, columns 11–12.

Red: 3 squares across rows 6–6, columns 1–3. It never leaves row 6, so its queen is locked to that row.

Teal covers 3 squares, spanning 2 rows and 2 columns (rows 11–12, columns 1–2).

Slate occupies 6 squares within rows 5–9, columns 11–12.

Rose: 7 squares across rows 10–12, columns 10–12.

Orange covers 8 squares, spanning 4 rows and 3 columns (rows 9–12, columns 1–3).

Indigo occupies 12 squares within rows 1–4, columns 6–11.

Khaki: 12 squares across rows 7–10, columns 1–5.

Mint covers 13 squares, spanning 5 rows and 4 columns (rows 2–6, columns 9–12).

Pale yellow occupies 19 squares within rows 5–10, columns 5–8.

Sea green: 26 squares across rows 6–12, columns 4–11.

Blue covers 32 squares, spanning 6 rows and 7 columns (rows 1–6, columns 1–7).

Where to start on this board

Begin where the choices are fewest. On this board that means amber, which owns just 3 squares inside a 2×2 window running from row 1 to row 2 and column 11 to column 12. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Amber spans 2 rows, so it stays open for now — but it is still the shortest list on the board at 3 squares. Work through those squares first and mark the ones that would leave another region homeless. That pruning is what makes the rest of the grid legible.

Work outward to the other flat regions next. Red 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 #263

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3 and 4 are the narrowest, touched by only 3 colors. Columns 4, 8 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 3 colors has to be claimed by one of them, which pushes every remaining region into the other 11 rows. Row 6, meeting 6 colors, is the opposite case — the busiest line on #263 and the last one you should expect to crack.

Working through the middle game

The middle of #263 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.

Resist the plausible-looking queen. On #263 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 #263 is rated easy

Ratings track how generous the opening is. On #263 you get one region pinned to a single row or column, a smallest color of 3 squares, a tightest row crossed by 3 colors, and a 29-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.

Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.

Stuck on #263 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.

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 #263 the place to look for one is around row 1.

Here is a shape check that gives nothing away: when #263 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 #263?

Puzzle #263 is rated easy. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.

Does 12x12 puzzle #263 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #263, 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 #263?

Start with the amber region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 11–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.