9x9 Queens Puzzle #212

Difficulty: easy. Place 9 queens on this 9x9 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 12-step reasoning is written out below.

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Step-by-step solution for puzzle #212

What follows is a complete solve of puzzle #212, worked the way a person works it rather than the way a computer does. It runs to 12 deductions — 9 queen placements and 3 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 region shadow.

Techniques this board needs: region shadow, last square in a region, region confined to one line.

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

  1. Step 1. Wherever blue ends up among its 3 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.

  2. Step 2. The slate region is down to one open square, at row 5, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 3, the remaining slate squares, and the ring of neighbours around row 5, column 3.

  3. Step 3. Only row 3, column 2 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 2, in blue and in the ring around that square is now dead.

  4. Step 4. The indigo region is down to one open square, at row 1, column 1. Every colour holds exactly one queen, so that square is forced. Row 1 and column 1 are now spoken for, along with the squares touching that queen.

    Puzzle #212 after step 4: 3 of 9 queens placed
    The board after step 4 — 3 of 9 queens placed.

  5. Step 5. Khaki is down to 4 candidates in rows 8 and 9, columns 4–6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about khaki itself.

  6. Step 6. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.

  7. Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: khaki has one square left, so its queen takes row 8, column 6; pale yellow has one square left, so its queen takes row 7, column 8; red has one square left, so its queen takes row 6, column 5; amber has one square left, so its queen takes row 2, column 4; orange has one square left, so its queen takes row 9, column 9; mint has one square left, so its queen takes row 4, column 7. 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 4, column 7.

    Puzzle #212 after step 7: 9 of 9 queens placed
    The board after step 7 — 9 of 9 queens placed.

That completes the board: 9 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 9x9 Queens puzzle #212

This is puzzle number 212 in the 9x9 collection, rated easy. The grid holds 81 squares split between nine colored regions, and a finished board carries nine queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.

There is exactly one way to finish #212, 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 nine regions is what sets the depth.

How the colors divide this board

From smallest to largest, the regions on puzzle #212 are: slate (2 squares), blue (3 squares), orange (3 squares), khaki (4 squares), pale yellow (5 squares), indigo (6 squares), amber (16 squares), mint (20 squares), red (22 squares). An even split would hand every color 9 squares, so the slate region is running 7 squares under that average while the red region is the roomiest area on the grid with 22 squares.

Every color takes one queen and one only, whatever its size — which is why the 20 square difference between slate 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.

A region's outline can constrain it more than its size does. Here slate is the most solid, filling 100% of its 1×2 box, and khaki the most diffuse at 67% of its 2×3 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.

Slate occupies 2 squares within rows 5–5, columns 2–3. It never leaves row 5, so its queen is locked to that row.

Blue: 3 squares across rows 3–4, columns 2–3.

Orange covers 3 squares, spanning 1 row and 3 columns (rows 9–9, columns 7–9). It never leaves row 9, so its queen is locked to that row.

Khaki occupies 4 squares within rows 8–9, columns 4–6.

Pale yellow: 5 squares across rows 7–8, columns 7–9.

Indigo covers 6 squares, spanning 4 rows and 2 columns (rows 1–4, columns 1–2).

Amber occupies 16 squares within rows 1–4, columns 3–8.

Mint: 20 squares across rows 1–7, columns 6–9.

Red covers 22 squares, spanning 5 rows and 6 columns (rows 5–9, columns 1–6).

Where to start on this board

Begin where the choices are fewest. On this board that means slate, which owns just 2 squares inside a 1×2 window running from row 5 to row 5 and column 2 to column 3. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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. Orange, blue, pale yellow and khaki 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 #212

A quick way to find the next move is to count how many different colors touch each line. On this board, row 6 is the narrowest, touched by only 2 colors. Column 1 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 2 colors, so one of that handful must take the row and the rest are squeezed into the other 8 rows. Row 4 sits at the far end with 4 colors crossing it; it will almost certainly be among the last to settle.

Working through the middle game

Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.

Keep alternating between two views of the board. In the region view you ask which of the nine 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 9x9 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 #212 is rated easy

Ratings track how generous the opening is. On #212 you get two regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 20-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.

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 #212 despite the easy 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 9x9

At 9x9 a full re-scan after every move starts to get slow, so work locally instead. Once a queen goes down, check only the regions, rows and columns that placement actually touched — that is where new information appeared. Fall back to a complete sweep only when the local pass turns up nothing, and your solve times will drop noticeably.

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 #212 is row 6.

Use this as a rough check on your progress: the completed board has 2 queens around the border and 7 queens in the middle, including 2 in corners. 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 9x9 Queens puzzle #212?

Puzzle #212 is rated easy. Its smallest color region holds 2 squares, 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 9x9 puzzle #212 have only one solution?

Yes. Every puzzle in the 9x9 collection, including #212, has been verified to have exactly one valid arrangement of nine queens, and it can always be reached by logic alone — no guessing or backtracking needed.

Where should I place my first queen on puzzle #212?

Start with the slate region — the most constrained color on this board, with 2 squares spanning rows 5–5 and columns 2–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.