12x12 Queens Puzzle #248

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 23-step reasoning is written out below.

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Step-by-step solution for puzzle #248

What follows is a complete solve of puzzle #248, worked the way a person works it rather than the way a computer does. It runs to 23 deductions — 12 queen placements and 11 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: last square in a region, region shadow, region confined to one line, pairing argument on rows, pairing argument on columns.

Show the full walkthrough (16 steps) — contains the solution

  1. Step 1. Only row 4, column 1 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 1, the rest of the mint region and every square adjacent to it — diagonals included.

  2. Step 2. The khaki region is down to one open square, at row 8, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 3, the remaining khaki squares, and the ring of neighbours around row 8, column 3.

  3. Step 3. The indigo region has 4 squares left, spread across rows 1 and 2, columns 10–12. 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.

  4. Step 4. Wherever slate ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

  5. Step 5. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 7 squares in all.

    Puzzle #248 after step 5: 2 of 12 queens placed
    The board after step 5 — 2 of 12 queens placed.

  6. Step 6. The sea green region has 4 squares left, spread across rows 10 and 11, columns 2, 4, and 5. 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. Wherever rose ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

  8. Step 8. Here is the pairing argument. The teal and rose regions have no open squares outside rows 11 and 12 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 13 squares come off in one stroke.

  9. Step 9. Sea green cannot leave row 10 — every one of its open squares (2 open squares) sits there. That row belongs to sea green, so every square on it owned by another colour is dead: 7 squares in all.

  10. Step 10. All of the orange region's remaining squares (3 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.

  11. Step 11. Pale yellow is down to 4 candidates in rows 6 and 7, columns 4–6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.

    Puzzle #248 after step 11: 2 of 12 queens placed
    The board after step 11 — 2 of 12 queens placed.

  12. Step 12. Here is the pairing argument. The slate and rose 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: 7 squares come off in one stroke.

  13. Step 13. Only row 1, column 10 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 10, the rest of the indigo region and every square adjacent to it — diagonals included.

  14. Step 14. The orange region is down to one open square, at row 9, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 8, the remaining orange squares, and the ring of neighbours around row 9, column 8.

  15. Step 15. Sea green and teal are now boxed into columns 2 and 4 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 6 squares at once.

  16. Step 16. 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: blue has one square left, so its queen takes row 3, column 5; pale yellow has one square left, so its queen takes row 7, column 6; red has one square left, so its queen takes row 6, column 9; 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 7; rose has one square left, so its queen takes row 12, column 11; teal has one square left, so its queen takes row 11, column 2; sea green has one square left, so its queen takes row 10, 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 10, column 4.

    Puzzle #248 after step 16: 12 of 12 queens placed
    The board after step 16 — 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 #248

This is puzzle number 248 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.

Puzzle #248 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 #248 are: mint (1 square), khaki (1 square), rose (3 squares), indigo (4 squares), slate (8 squares), teal (8 squares), sea green (12 squares), pale yellow (14 squares), amber (20 squares), blue (24 squares), orange (24 squares), red (25 squares). An even split would hand every color 12 squares, so the mint region is running 11 squares under that average while the red region is the roomiest area on the grid with 25 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Mint is working with 1 square while red has 25 to spare, a gap of 24. Attack the cramped end and the roomy regions tend to resolve themselves.

Shape matters as much as size. The mint region is the most compact color here, filling 100% of the 1×1 box that encloses it, while sea green is the most scattered at 48% of its 5×5 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

Here is the full footprint of every color on puzzle #248, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Mint occupies 1 square within rows 4–4, columns 1–1. It never leaves row 4, so its queen is locked to that row.

Khaki: 1 square across rows 8–8, columns 3–3. It never leaves row 8, so its queen is locked to that row.

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

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

Slate: 8 squares across rows 2–8, columns 11–12.

Teal covers 8 squares, spanning 3 rows and 4 columns (rows 10–12, columns 1–4).

Sea green occupies 12 squares within rows 7–11, columns 1–5.

Pale yellow: 14 squares across rows 6–10, columns 3–7.

Amber covers 20 squares, spanning 6 rows and 5 columns (rows 1–6, columns 5–9).

Blue occupies 24 squares within rows 1–7, columns 1–5.

Orange: 24 squares across rows 8–12, columns 5–12.

Red covers 25 squares, spanning 9 rows and 5 columns (rows 1–9, columns 7–11).

Where to start on this board

The most constrained color is where a solve should begin, and on #248 that is mint with 1 square. It reaches from row 4 to row 4 and from column 1 to column 1 — 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 mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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. Khaki, indigo 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 #248

A quick way to find the next move is to count how many different colors touch each line. On this board, row 12 is the narrowest, touched by only 3 colors. Columns 2, 6, 8, 9 and 10 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 8, meeting 6 colors, is the opposite case — the busiest line on #248 and the last one you should expect to crack.

Working through the middle game

Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.

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 #248 is rated easy

The rating reflects how much the board concedes up front. Puzzle #248 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 24 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

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.

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 row 12 on this board.

Here is a shape check that gives nothing away: when #248 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 #248?

Puzzle #248 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 #248 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #248, 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 #248?

Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.