12x12 Queens Puzzle #213

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 18-step reasoning is written out below.

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Step-by-step solution for puzzle #213

What follows is a complete solve of puzzle #213, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 12 queen placements and 6 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: region shadow, pairing argument on rows, region confined to one line, last square in a row, last square in a region, last square in a column.

Show the full walkthrough (7 steps) — contains the solution

  1. Step 1. Wherever amber ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.

  2. Step 2. Red is down to 6 candidates in rows 2–6, columns 11 and 12, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about red itself.

  3. Step 3. The sea green region has 5 squares left, spread across rows 10–12, columns 1–3. 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 rose ends up among its 7 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

    Puzzle #213 after step 4: 0 of 12 queens placed
    The board after step 4 — 0 of 12 queens placed.

  5. Step 5. Indigo, amber, and blue are now boxed into rows 1–3 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 15 squares at once.

  6. Step 6. All of the mint region's remaining squares (2 open squares) lie in row 4. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 13 squares come off.

  7. Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 12 queens fall out in order without any new idea being needed: row 3 is down to one square, putting a queen on row 3, column 7; slate has one square left, so its queen takes row 5, column 6; red has one square left, so its queen takes row 6, column 12; rose has one square left, so its queen takes row 12, column 8; teal has one square left, so its queen takes row 11, column 10; sea green has one square left, so its queen takes row 10, column 1; orange has one square left, so its queen takes row 9, column 4; amber has one square left, so its queen takes row 2, column 3; mint has one square left, so its queen takes row 4, column 2; column 5 is down to one square, putting a queen on row 7, column 5; khaki has one square left, so its queen takes row 8, column 11; 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.

    Puzzle #213 after step 7: 12 of 12 queens placed
    The board after step 7 — 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 #213

Puzzle #213 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 #213, 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 #213 are: amber (4 squares), sea green (5 squares), red (6 squares), orange (6 squares), indigo (7 squares), rose (7 squares), blue (8 squares), mint (9 squares), teal (11 squares), slate (17 squares), khaki (23 squares), pale yellow (41 squares). An even split would hand every color 12 squares, so the amber region is running 8 squares under that average while the pale yellow region is the roomiest area on the grid with 41 squares.

Every color takes one queen and one only, whatever its size — which is why the 37 square difference between amber and pale yellow 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. Mint is the tidiest shape on #213, packing 75% of its 4×3 bounding box, whereas teal straggles across its 4×6 box at just 46%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Here is the full footprint of every color on puzzle #213, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Amber: 4 squares across rows 1–3, columns 3–4.

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

Red occupies 6 squares within rows 2–6, columns 11–12.

Orange: 6 squares across rows 9–12, columns 2–4.

Indigo covers 7 squares, spanning 3 rows and 5 columns (rows 1–3, columns 8–12).

Rose occupies 7 squares within rows 9–12, columns 6–8.

Blue: 8 squares across rows 1–3, columns 5–8.

Mint covers 9 squares, spanning 4 rows and 3 columns (rows 1–4, columns 1–3).

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

Slate: 17 squares across rows 2–5, columns 4–10.

Khaki covers 23 squares, spanning 7 rows and 5 columns (rows 5–11, columns 8–12).

Pale yellow occupies 41 squares within rows 4–12, columns 1–9.

Where to start on this board

Open on the tightest color. Here that is amber, confined to 4 squares between rows 1 and 3 and columns 3 and 4. Its queen has nowhere else to go, which means those 3 rows and 2 columns carry more constraint than anywhere else on #213.

With 3 rows and 2 columns of room, amber needs narrowing rather than solving outright. Test its 4 squares against the neighbours: a candidate that would strand another color is dead, and eliminating even two of them tightens the whole corner of the board around rows 1–3.

No region here is pinned to a shallow band of rows, so turn the same idea sideways: amber and red span 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 #213

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 7 and 8 are the narrowest, touched by only 2 colors. Columns 1 and 5 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 11 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.

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.

With twelve queens to seat and twelve regions competing over 144 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 12x12 boards quickly and players who stall halfway.

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 #213 is rated medium

The rating reflects how much the board concedes up front. Puzzle #213 has no region confined to a single row or column, its smallest color holds 4 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 37 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a medium board from the rest.

Stuck on #213 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 #213 is row 7.

As a sanity check rather than a spoiler: the finished solution to #213 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 #213?

Puzzle #213 is rated medium. Its smallest color region holds 4 squares, its tightest row is touched by 2 colors, and no region is confined to a single row or column, so the opening move takes some hunting.

Does 12x12 puzzle #213 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #213, 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 #213?

Start with the amber region — the most constrained color on this board, with 4 squares spanning rows 1–3 and columns 3–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.