12x12 Queens Puzzle #290

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 17-step reasoning is written out below.

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Step-by-step solution for puzzle #290

What follows is a complete solve of puzzle #290, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 12 queen placements and 5 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 rows.

Techniques this board needs: last square in a region, region confined to one line, pairing argument on rows.

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

  1. Step 1. Only row 8, column 12 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 12, the rest of the khaki region and every square adjacent to it — diagonals included.

  2. Step 2. The slate region is down to one open square, at row 5, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 11, the remaining slate squares, and the ring of neighbours around row 5, column 11.

  3. Step 3. Only row 12, column 10 is still open in rose, and since each colour must take a queen, that settles it. Everything else in row 12, in column 10, in rose and in the ring around that square is now dead.

  4. Step 4. 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: 9 squares come off.

    Puzzle #290 after step 4: 3 of 12 queens placed
    The board after step 4 — 3 of 12 queens placed.

  5. Step 5. Only row 2, column 5 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 5, the rest of the amber region and every square adjacent to it — diagonals included.

  6. Step 6. All of the orange region's remaining squares (4 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.

  7. Step 7. Only row 1, column 7 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 7, in indigo and in the ring around that square is now dead.

    Puzzle #290 after step 7: 5 of 12 queens placed
    The board after step 7 — 5 of 12 queens placed.

  8. Step 8. All of the sea green region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.

  9. Step 9. Sea green and teal are now boxed into rows 10 and 11 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 4 squares at once.

  10. Step 10. Here is the pairing argument. The pale yellow and orange regions have no open squares outside rows 7 and 9 — 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: 5 squares come off in one stroke.

  11. Step 11. 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: red has one square left, so its queen takes row 6, column 9; mint has one square left, so its queen takes row 4, column 6; orange has one square left, so its queen takes row 9, column 8; pale yellow has one square left, so its queen takes row 7, column 4; teal has one square left, so its queen takes row 11, column 3; blue has one square left, so its queen takes row 3, column 2; sea green has one square left, so its queen takes row 10, column 1. 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 1.

    Puzzle #290 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 #290

Board #290 of the 12x12 bank carries a easy 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.

Like every board on this site, #290 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.

How the colors divide this board

From smallest to largest, the regions on puzzle #290 are: khaki (1 square), indigo (2 squares), slate (3 squares), rose (3 squares), amber (4 squares), sea green (5 squares), teal (12 squares), pale yellow (16 squares), red (20 squares), orange (21 squares), blue (27 squares), mint (30 squares). An even split would hand every color 12 squares, so the khaki region is running 11 squares under that average while the mint region is the roomiest area on the grid with 30 squares.

Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So khaki, with 1 square, is under far more pressure than mint with 30. A 29-square gap like this one rewards players who start where the choices are fewest.

Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×2 frame; red is the loosest, occupying only 48% of its 6×7 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

Region by region

Below is every color on #290 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.

Khaki occupies 1 square within rows 8–8, columns 12–12. It never leaves row 8, so its queen is locked to that row.

Indigo: 2 squares across rows 1–1, columns 7–8. It never leaves row 1, so its queen is locked to that row.

Slate covers 3 squares, spanning 2 rows and 2 columns (rows 4–5, columns 11–12).

Rose occupies 3 squares within rows 12–12, columns 10–12. It never leaves row 12, so its queen is locked to that row.

Amber: 4 squares across rows 1–2, columns 4–6.

Sea green covers 5 squares, spanning 3 rows and 3 columns (rows 10–12, columns 1–3).

Teal occupies 12 squares within rows 10–12, columns 2–7.

Pale yellow: 16 squares across rows 7–10, columns 1–6.

Red covers 20 squares, spanning 6 rows and 7 columns (rows 5–10, columns 6–12).

Orange occupies 21 squares within rows 7–12, columns 6–12.

Blue: 27 squares across rows 1–7, columns 1–5.

Mint covers 30 squares, spanning 6 rows and 8 columns (rows 1–6, columns 5–12).

Where to start on this board

Khaki is the natural opening on #290: it is the smallest region on the grid at 1 square, boxed into rows 8–8 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 khaki never leaves row 8, its queen must be in that row — and that instantly settles row 8 for everyone else. Sweep along it and X out every square that is not khaki. 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, amber and slate 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 #290

A quick way to find the next move is to count how many different colors touch each line. On this board, row 3 is the narrowest, touched by only 2 colors. Columns 1 and 9 are the tightest columns, with 3 colors.

Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 11 rows. By contrast row 10 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 #290 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.

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 #290 is rated easy

What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 29. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

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.

If #290 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.

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.

Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #290, start hunting for it near row 3.

As a sanity check rather than a spoiler: the finished solution to #290 puts 4 queens on the outer border and 8 queens in the interior, with none in a 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 #290?

Puzzle #290 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.

Does 12x12 puzzle #290 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #290, 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 #290?

Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 12–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.