12x12 Queens Puzzle #229

Difficulty: medium. 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 20-step reasoning is written out below.

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Step-by-step solution for puzzle #229

What follows is a complete solve of puzzle #229, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 12 queen placements and 8 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 shadow, pairing argument on rows, region confined to one line.

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

  1. Step 1. Only row 7, column 1 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 1, the rest of the pale yellow region and every square adjacent to it — diagonals included.

  2. Step 2. Sea green is down to 4 candidates in rows 10–12, columns 2 and 3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about sea green itself.

  3. Step 3. The rose region has 3 squares left, spread across rows 11 and 12, columns 11 and 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. Here is the pairing argument. The sea green, teal, and rose regions have no open squares outside rows 10–12 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 14 squares come off in one stroke.

    Puzzle #229 after step 4: 1 of 12 queens placed
    The board after step 4 — 1 of 12 queens placed.

  5. Step 5. Khaki and orange are now boxed into rows 8 and 9 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 8 squares at once.

  6. Step 6. The red region has 3 squares left, spread across rows 5 and 6, columns 3 and 4. 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. Slate and red are now boxed into rows 5 and 6 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 9 squares at once.

    Puzzle #229 after step 7: 1 of 12 queens placed
    The board after step 7 — 1 of 12 queens placed.

  8. Step 8. 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: mint has one square left, so its queen takes row 4, column 12; rose has one square left, so its queen takes row 12, column 11; khaki has one square left, so its queen takes row 8, column 10; indigo has one square left, so its queen takes row 1, 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 1, column 9.

  9. Step 9. 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: 1 square come off.

  10. Step 10. Sea green cannot leave column 3 — 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: 6 squares in all.

  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 4; slate has one square left, so its queen takes row 5, column 7; teal has one square left, so its queen takes row 11, column 8; orange has one square left, so its queen takes row 9, column 6; amber has one square left, so its queen takes row 2, column 5; 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 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 10, column 3.

    Puzzle #229 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 #229

Puzzle #229 is one of the medium-rated boards in the 12x12 set. Twelve colors divide its 144 squares, and you win by placing twelve queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.

There is exactly one way to finish #229, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these twelve regions is what sets the depth.

How the colors divide this board

From smallest to largest, the regions on puzzle #229 are: pale yellow (1 square), rose (3 squares), mint (6 squares), slate (8 squares), sea green (10 squares), teal (10 squares), indigo (14 squares), orange (16 squares), amber (18 squares), khaki (18 squares), blue (20 squares), red (20 squares). An even split would hand every color 12 squares, so the pale yellow region is running 11 squares under that average while the red region is the roomiest area on the grid with 20 squares.

Every color takes one queen and one only, whatever its size — which is why the 19 square difference between pale yellow and red is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.

Square count is only half the story — how a color is arranged counts too. Pale yellow is the tidiest shape on #229, packing 100% of its 1×1 bounding box, whereas indigo straggles across its 5×6 box at just 47%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a medium board.

Pale yellow covers 1 square, spanning 1 row and 1 column (rows 7–7, columns 1–1). It never leaves row 7, so its queen is locked to that row.

Rose occupies 3 squares within rows 11–12, columns 11–12.

Mint: 6 squares across rows 4–6, columns 10–12.

Slate covers 8 squares, spanning 2 rows and 6 columns (rows 5–6, columns 5–10).

Sea green occupies 10 squares within rows 8–12, columns 1–3.

Teal: 10 squares across rows 10–12, columns 4–8.

Indigo covers 14 squares, spanning 5 rows and 6 columns (rows 1–5, columns 7–12).

Orange occupies 16 squares within rows 7–11, columns 5–10.

Amber: 18 squares across rows 1–4, columns 4–10.

Khaki covers 18 squares, spanning 6 rows and 5 columns (rows 7–12, columns 8–12).

Blue occupies 20 squares within rows 1–5, columns 1–6.

Red: 20 squares across rows 5–11, columns 1–6.

Where to start on this board

Open on the tightest color. Here that is pale yellow, confined to 1 square between rows 7 and 7 and columns 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #229.

Because pale yellow never leaves row 7, its queen must be in that row — and that instantly settles row 7 for everyone else. Sweep along it and X out every square that is not pale yellow. 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. Slate 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 #229

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3 and 6 are the narrowest, touched by only 3 colors. Columns 2 and 3 are the tightest columns, with 3 colors.

A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 11 rows. Row 11 is the crowded extreme at 6 colors — worth revisiting later, not now.

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 #229 is rated medium

The medium label comes out of four measurable things about #229: two of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 19. Boards that score tight on those measures give up their first queen fast.

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.

Stuck on #229 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.

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.

There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #229 is row 1.

A non-spoiling distribution check: solved, #229 carries 4 queens on the perimeter against 8 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.

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 #229?

Puzzle #229 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.

Does 12x12 puzzle #229 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #229, 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 #229?

Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.