12x12 Queens Puzzle #288

Difficulty: hard. 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 21-step reasoning is written out below.

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Step-by-step solution for puzzle #288

What follows is a complete solve of puzzle #288, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 12 queen placements and 9 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 confined to one line, region shadow, last square in a region, pairing argument on rows, pairing argument on columns, last square in a row.

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

  1. Step 1. 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: 10 squares in all.

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

  3. Step 3. The mint region has 6 squares left, spread across rows 2–5, columns 3–5. 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.

  4. Step 4. Wherever sea green 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.

    Puzzle #288 after step 4: 0 of 12 queens placed
    The board after step 4 — 0 of 12 queens placed.

  5. Step 5. Teal cannot leave row 11 — every one of its open squares (2 open squares) sits there. That row belongs to teal, so every square on it owned by another colour is dead: 14 squares in all.

  6. Step 6. 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: sea green has one square left, so its queen takes row 10, column 12; rose has one square left, so its queen takes row 12, column 11; indigo has one square left, so its queen takes row 1, column 10; teal has one square left, so its queen takes row 11, column 9. 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 11, column 9.

  7. Step 7. 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.

    Puzzle #288 after step 7: 4 of 12 queens placed
    The board after step 7 — 4 of 12 queens placed.

  8. Step 8. Amber and blue are now boxed into rows 2 and 3 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 6 squares at once.

  9. Step 9. All of the mint region's remaining squares (2 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 8 squares come off.

  10. Step 10. Amber, pale yellow, and orange are now boxed into columns 6–8 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 6 squares at once.

  11. Step 11. 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: red has one square left, so its queen takes row 6, column 4; mint has one square left, so its queen takes row 4, column 5; row 3 is down to one square, putting a queen on row 3, column 1; slate has one square left, so its queen takes row 5, column 2; pale yellow has one square left, so its queen takes row 7, column 8; amber has one square left, so its queen takes row 2, column 6; orange has one square left, so its queen takes row 9, column 7; khaki has one square left, so its queen takes row 8, 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 8, column 3.

    Puzzle #288 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 #288

This is puzzle number 288 in the 12x12 collection, rated hard. 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.

As with every puzzle in this collection, #288 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.

How the colors divide this board

From smallest to largest, the regions on puzzle #288 are: teal (2 squares), indigo (3 squares), sea green (3 squares), rose (4 squares), blue (6 squares), mint (9 squares), slate (13 squares), red (13 squares), amber (21 squares), khaki (22 squares), pale yellow (23 squares), orange (25 squares). An even split would hand every color 12 squares, so the teal region is running 10 squares under that average while the orange 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. Teal is working with 2 squares while orange has 25 to spare, a gap of 23. 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 1×3 box that encloses it, while red is the most scattered at 43% of its 6×5 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

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.

Teal: 2 squares across rows 11–11, columns 9–10. It never leaves row 11, so its queen is locked to that row.

Indigo covers 3 squares, spanning 1 row and 3 columns (rows 1–1, columns 10–12). It never leaves row 1, so its queen is locked to that row.

Sea green occupies 3 squares within rows 10–11, columns 11–12.

Rose: 4 squares across rows 12–12, columns 9–12. It never leaves row 12, so its queen is locked to that row.

Blue covers 6 squares, spanning 3 rows and 3 columns (rows 1–3, columns 1–3).

Mint occupies 9 squares within rows 1–5, columns 2–5.

Slate: 13 squares across rows 4–9, columns 1–4.

Red covers 13 squares, spanning 6 rows and 5 columns (rows 2–7, columns 4–8).

Amber occupies 21 squares within rows 1–4, columns 5–12.

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

Pale yellow covers 23 squares, spanning 6 rows and 6 columns (rows 5–10, columns 7–12).

Orange occupies 25 squares within rows 7–12, columns 4–10.

Where to start on this board

The most constrained color is where a solve should begin, and on #288 that is teal with 2 squares. It reaches from row 11 to row 11 and from column 9 to column 10 — 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 teal never leaves row 11, its queen must be in that row — and that instantly settles row 11 for everyone else. Sweep along it and X out every square that is not teal. 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, rose and sea green 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 #288

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 6 and 12 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, 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 7, meeting 5 colors, is the opposite case — the busiest line on #288 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 #288 is rated hard

Ratings track how generous the opening is. On #288 you get three regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 3 colors, and a 23-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.

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.

A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.

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 6 on this board.

Here is a shape check that gives nothing away: when #288 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 #288?

Puzzle #288 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.

Does 12x12 puzzle #288 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #288, 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 #288?

Start with the teal region — the most constrained color on this board, with 2 squares spanning rows 11–11 and columns 9–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.