12x12 Queens Puzzle #286

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 22-step reasoning is written out below.

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Step-by-step solution for puzzle #286

What follows is a complete solve of puzzle #286, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 12 queen placements and 10 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 2, column 12 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 12, the rest of the amber region and every square adjacent to it — diagonals included.

  2. Step 2. The rose region is down to one open square, at row 12, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 12 and column 2, the remaining rose squares, and the ring of neighbours around row 12, column 2.

  3. Step 3. Only row 1, column 1 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 1, in indigo and in the ring around that square is now dead.

  4. Step 4. Wherever red 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. Pale yellow cannot leave column 10 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 11 squares in all.

    Puzzle #286 after step 5: 3 of 12 queens placed
    The board after step 5 — 3 of 12 queens placed.

  6. Step 6. The orange region has 4 squares left, spread across rows 7–9, columns 3 and 4. 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.

  7. Step 7. Blue, mint, slate, and red are now boxed into rows 3–6 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 3 squares at once.

  8. Step 8. The pale yellow region is down to one open square, at row 7, column 10. Every colour holds exactly one queen, so that square is forced. Row 7 and column 10 are now spoken for, along with the squares touching that queen.

  9. Step 9. Orange cannot leave column 4 — every one of its open squares (2 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 7 squares in all.

  10. Step 10. All of the mint region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.

  11. Step 11. Red cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 6 squares in all.

    Puzzle #286 after step 11: 4 of 12 queens placed
    The board after step 11 — 4 of 12 queens placed.

  12. Step 12. The slate region has 4 squares left, spread across rows 3–5, 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.

  13. Step 13. Khaki cannot leave row 8 — every one of its open squares (2 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 4 squares in all.

  14. Step 14. The orange region is down to one open square, at row 9, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 4, the remaining orange squares, and the ring of neighbours around row 9, column 4.

  15. Step 15. Slate and khaki are now boxed into columns 6 and 7 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 5 squares at once.

  16. Step 16. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: sea green has one square left, so its queen takes row 10, column 8; teal has one square left, so its queen takes row 11, column 11; blue has one square left, so its queen takes row 3, column 9; mint has one square left, so its queen takes row 4, column 3; slate has one square left, so its queen takes row 5, column 7; red has one square left, so its queen takes row 6, column 5; khaki has one square left, so its queen takes row 8, 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 8, column 6.

    Puzzle #286 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 #286

Board #286 of the 12x12 bank carries a hard rating. Its 144 squares are shared between twelve colored regions, and the solution places twelve queens: one per row, one per column, one per region, none of them side by side or corner to corner.

As with every puzzle in this collection, #286 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 #286 are: amber (1 square), rose (1 square), pale yellow (2 squares), indigo (6 squares), red (6 squares), sea green (14 squares), mint (15 squares), slate (15 squares), khaki (18 squares), orange (19 squares), teal (19 squares), blue (28 squares). An even split would hand every color 12 squares, so the amber region is running 11 squares under that average while the blue region is the roomiest area on the grid with 28 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 1 place to put its queen; blue has 28. The spread between them on this board is 27 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 amber is the most solid, filling 100% of its 1×1 box, and khaki the most diffuse at 37% of its 7×7 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

Here is the full footprint of every color on puzzle #286, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

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

Rose occupies 1 square within rows 12–12, columns 2–2. It never leaves row 12, so its queen is locked to that row.

Pale yellow: 2 squares across rows 6–7, columns 10–10. It sits wholly inside column 10, so its queen must be in that column.

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

Red occupies 6 squares within rows 5–6, columns 2–5.

Sea green: 14 squares across rows 8–12, columns 4–9.

Mint covers 15 squares, spanning 7 rows and 4 columns (rows 1–7, columns 1–4).

Slate occupies 15 squares within rows 1–6, columns 5–8.

Khaki: 18 squares across rows 4–10, columns 3–9.

Orange covers 19 squares, spanning 6 rows and 6 columns (rows 7–12, columns 1–6).

Teal occupies 19 squares within rows 8–12, columns 8–12.

Blue: 28 squares across rows 1–7, columns 7–12.

Where to start on this board

Amber is the natural opening on #286: it is the smallest region on the grid at 1 square, boxed into rows 2–2 and columns 12–12. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.

Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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. Rose, red and pale yellow 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 #286

A quick way to find the next move is to count how many different colors touch each line. On this board, row 11 is the narrowest, touched by only 3 colors. Column 11 is the tightest column, with 2 colors.

Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 11 rows. Row 6 sits at the far end with 6 colors crossing it; it will almost certainly be among the last to settle.

Working through the middle game

After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.

The whole middle game reduces to two sweeps. Sweep the twelve colors looking for one with a single square left; sweep the twelve rows and twelve columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 12x12 solve from a stalled one.

The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.

Why puzzle #286 is rated hard

The rating reflects how much the board concedes up front. Puzzle #286 has five 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 27 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

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.

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.

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 #286 the place to look for one is around column 11.

Use this as a rough check on your progress: the completed board has 3 queens around the border and 9 queens in the middle, including 1 in a corner. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.

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 #286?

Puzzle #286 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.

Does 12x12 puzzle #286 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #286, 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 #286?

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