12x12 Queens Puzzle #230

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 37-step reasoning is written out below.

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Step-by-step solution for puzzle #230

What follows is a complete solve of puzzle #230, worked the way a person works it rather than the way a computer does. It runs to 37 deductions — 12 queen placements and 25 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 proof by contradiction.

Techniques this board needs: last square in a region, region shadow, region confined to one line, pairing argument on columns, proof by contradiction, line confined to one region, last square in a row.

Show the full walkthrough (34 steps) — contains the solution

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

  2. Step 2. The pale yellow region is down to one open square, at row 7, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 11, the remaining pale yellow squares, and the ring of neighbours around row 7, column 11.

  3. Step 3. The blue region has 5 squares left, spread across rows 2–4, columns 8–10. 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. All of the red region's remaining squares (3 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.

  5. Step 5. Blue is down to 2 candidates in rows 2 and 3, columns 8 and 10, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about blue itself.

  6. Step 6. Here is the pairing argument. The blue, mint, and rose regions have no open squares outside columns 7, 8, and 10 — 3 colours confined to 3 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.

  7. Step 7. Sea green cannot leave column 6 — every one of its open squares (2 open squares) sits there. That column belongs to sea green, so every square in it owned by another colour is dead: 10 squares in all.

  8. Step 8. Khaki is down to 5 candidates in rows 8–11, columns 4 and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about khaki itself.

  9. Step 9. Test row 2, column 1 for amber: place a queen there, run the forced consequences through, and column 4 runs out of open squares entirely. The assumption breaks, so the square is eliminated.

    Puzzle #230 after step 9: 2 of 12 queens placed
    The board after step 9 — 2 of 12 queens placed.

  10. Step 10. Now a short proof by contradiction. Suppose the amber queen went to row 2, column 2. Follow the forced moves that would create and row 5 runs out of open squares entirely — impossible. So that square is ruled out for good.

  11. Step 11. Test row 2, column 3 for amber: place a queen there, run the forced consequences through, and row 5 runs out of open squares entirely. The assumption breaks, so the square is eliminated.

  12. Step 12. Now a short proof by contradiction. Suppose the amber queen went to row 3, column 5. Follow the forced moves that would create and row 6 runs out of open squares entirely — impossible. So that square is ruled out for good.

  13. Step 13. Test row 4, column 2 for amber: place a queen there, run the forced consequences through, and the teal region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.

  14. Step 14. Now a short proof by contradiction. Suppose the amber queen went to row 4, column 3. Follow the forced moves that would create and the rose region is left with nowhere to put its queen — impossible. So that square is ruled out for good.

  15. Step 15. Amber and khaki are now boxed into columns 4 and 5 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 4 squares at once.

  16. Step 16. Now a short proof by contradiction. Suppose the amber queen went to row 4, column 4. Follow the forced moves that would create and row 6 runs out of open squares entirely — impossible. So that square is ruled out for good.

  17. Step 17. Test row 4, column 5 for amber: place a queen there, run the forced consequences through, and row 6 runs out of open squares entirely. The assumption breaks, so the square is eliminated.

    Puzzle #230 after step 17: 2 of 12 queens placed
    The board after step 17 — 2 of 12 queens placed.

  18. Step 18. Now a short proof by contradiction. Suppose the amber queen went to row 5, column 4. Follow the forced moves that would create and row 3 runs out of open squares entirely — impossible. So that square is ruled out for good.

  19. Step 19. Test row 5, column 5 for amber: place a queen there, run the forced consequences through, and row 3 runs out of open squares entirely. The assumption breaks, so the square is eliminated.

  20. Step 20. Now a short proof by contradiction. Suppose the amber queen went to row 6, column 4. Follow the forced moves that would create and the orange region is left with nowhere to put its queen — impossible. So that square is ruled out for good.

  21. Step 21. Amber cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 2 squares in all.

  22. Step 22. Now a short proof by contradiction. Suppose the amber queen went to row 6, column 5. Follow the forced moves that would create and row 3 runs out of open squares entirely — impossible. So that square is ruled out for good.

  23. Step 23. Only row 2, column 5 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 5, in amber and in the ring around that square is now dead.

  24. Step 24. The blue region is down to one open square, at row 3, column 8. Every colour holds exactly one queen, so that square is forced. Row 3 and column 8 are now spoken for, along with the squares touching that queen.

  25. Step 25. Test row 5, column 10 for mint: place a queen there, run the forced consequences through, and row 6 runs out of open squares entirely. The assumption breaks, so the square is eliminated.

  26. Step 26. Every open square left in row 5 (3 open squares) belongs to the slate region. Since that row must contain a queen, slate is the colour that supplies it — so slate squares anywhere else on the board are out, 6 squares in all.

    Puzzle #230 after step 26: 4 of 12 queens placed
    The board after step 26 — 4 of 12 queens placed.

  27. Step 27. 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: row 4 is down to one square, putting a queen on row 4, column 10; rose has one square left, so its queen takes row 12, column 7; sea green has one square left, so its queen takes row 10, column 6; row 6 is down to one square, putting a queen on row 6, 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 6, column 9.

  28. Step 28. Teal cannot leave column 3 — every one of its open squares (2 open squares) sits there. That column belongs to teal, so every square in it owned by another colour is dead: 2 squares in all.

  29. Step 29. Now a short proof by contradiction. Suppose the slate queen went to row 5, column 2. Follow the forced moves that would create and the teal region is left with nowhere to put its queen — impossible. So that square is ruled out for good.

  30. Step 30. Only row 5, column 1 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 1, the rest of the slate region and every square adjacent to it — diagonals included.

  31. Step 31. Now a short proof by contradiction. Suppose the khaki queen went to row 11, column 4. Follow the forced moves that would create and the orange region is left with nowhere to put its queen — impossible. So that square is ruled out for good.

  32. Step 32. 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.

  33. Step 33. The teal region is down to one open square, at row 11, column 3. Every colour holds exactly one queen, so that square is forced. Row 11 and column 3 are now spoken for, along with the squares touching that queen.

  34. Step 34. Only row 9, column 2 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 2, the rest of the orange region and every square adjacent to it — diagonals included.

    Puzzle #230 after step 34: 12 of 12 queens placed
    The board after step 34 — 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 #230

Board #230 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.

As with every puzzle in this collection, #230 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 #230 are: indigo (1 square), pale yellow (6 squares), orange (7 squares), red (10 squares), blue (11 squares), teal (11 squares), rose (11 squares), sea green (12 squares), khaki (13 squares), mint (16 squares), slate (16 squares), amber (30 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the amber 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 indigo, with 1 square, is under far more pressure than amber with 30. A 29-square gap like this one rewards players who start where the choices are fewest.

A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and red the most diffuse at 40% of its 5×5 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 #230, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

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

Pale yellow: 6 squares across rows 6–10, columns 11–12.

Orange covers 7 squares, spanning 4 rows and 3 columns (rows 8–11, columns 1–3).

Red occupies 10 squares within rows 6–10, columns 7–11.

Blue: 11 squares across rows 1–4, columns 8–12.

Teal covers 11 squares, spanning 4 rows and 6 columns (rows 9–12, columns 1–6).

Rose occupies 11 squares within rows 9–12, columns 7–12.

Sea green: 12 squares across rows 8–11, columns 6–9.

Khaki covers 13 squares, spanning 6 rows and 4 columns (rows 6–11, columns 3–6).

Mint occupies 16 squares within rows 3–7, columns 7–12.

Slate: 16 squares across rows 2–9, columns 1–4.

Amber covers 30 squares, spanning 6 rows and 8 columns (rows 1–6, columns 1–8).

Where to start on this board

Indigo is the natural opening on #230: it is the smallest region on the grid at 1 square, boxed into rows 1–1 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 indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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.

No region here is pinned to a shallow band of rows, so turn the same idea sideways: pale yellow spans only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.

The tightest lines on puzzle #230

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 2 colors. Column 5 is the tightest column, 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 9 meets 8 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 #230 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.

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.

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 #230 is rated easy

The rating reflects how much the board concedes up front. Puzzle #230 has two regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 29 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

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.

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 #230, start hunting for it near row 12.

As a sanity check rather than a spoiler: the finished solution to #230 puts 3 queens on the outer border and 9 queens in the interior, 1 of them in an actual 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 #230?

Puzzle #230 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.

Does 12x12 puzzle #230 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #230, 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 #230?

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