9x9 Queens Puzzle #219

Difficulty: hard. 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 16-step reasoning is written out below.

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Step-by-step solution for puzzle #219

What follows is a complete solve of puzzle #219, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 9 queen placements and 7 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 columns.

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

Show the full walkthrough (8 steps) — contains the solution

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

  2. Step 2. Orange is down to 3 candidates in rows 8 and 9, columns 8 and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about orange itself.

  3. Step 3. Indigo and amber are now boxed into rows 1 and 2 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 7 squares at once.

  4. Step 4. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.

    Puzzle #219 after step 4: 0 of 9 queens placed
    The board after step 4 — 0 of 9 queens placed.

  5. Step 5. Mint cannot leave row 4 — every one of its open squares (3 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 6 squares in all.

  6. Step 6. All of the slate region's remaining squares (5 open squares) lie in row 5. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.

  7. Step 7. Amber and orange are now boxed into columns 8 and 9 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.

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

    Puzzle #219 after step 8: 9 of 9 queens placed
    The board after step 8 — 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 #219

9x9 puzzle #219 is rated hard. Nine colored regions cover its 81 squares, and your job is to seat nine queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.

Puzzle #219 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.

How the colors divide this board

From smallest to largest, the regions on puzzle #219 are: amber (3 squares), orange (3 squares), indigo (7 squares), blue (7 squares), mint (8 squares), slate (9 squares), pale yellow (10 squares), red (16 squares), khaki (18 squares). An even split would hand every color 9 squares, so the amber region is running 6 squares under that average while the khaki region is the roomiest area on the grid with 18 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Amber has only 3 places to put its queen; khaki has 18. The spread between them on this board is 15 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

Shape matters as much as size. The pale yellow region is the most compact color here, filling 83% of the 4×3 box that encloses it, while slate is the most scattered at 50% of its 3×6 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.

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.

Amber: 3 squares across rows 1–2, columns 8–9.

Orange covers 3 squares, spanning 2 rows and 2 columns (rows 8–9, columns 8–9).

Indigo occupies 7 squares within rows 1–2, columns 1–5.

Blue: 7 squares across rows 1–3, columns 5–7.

Mint covers 8 squares, spanning 3 rows and 4 columns (rows 2–4, columns 2–5).

Slate occupies 9 squares within rows 3–5, columns 1–6.

Pale yellow: 10 squares across rows 6–9, columns 1–3.

Red covers 16 squares, spanning 6 rows and 4 columns (rows 2–7, columns 6–9).

Khaki occupies 18 squares within rows 6–9, columns 3–8.

Where to start on this board

Amber is the natural opening on #219: it is the smallest region on the grid at 3 squares, boxed into rows 1–2 and columns 8–9. Since one of those squares must hold a queen, that block of 2 rows and 2 columns is the most contested part of the board.

Amber spans 2 rows, so it stays open for now — but it is still the shortest list on the board at 3 squares. Work through those squares first and mark the ones that would leave another region homeless. That pruning is what makes the rest of the grid legible.

Work outward to the other flat regions next. Indigo and orange 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 #219

A quick way to find the next move is to count how many different colors touch each line. On this board, row 5 is the narrowest, touched by only 2 colors. Columns 1, 7 and 9 are the tightest columns, with 3 colors.

A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 8 rows. Row 2 is the crowded extreme at 5 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.

Two checks, run alternately, will carry you through the 81 squares of this grid. First: has any of the nine regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 9x9 boards almost always run one of those checks and forget the other.

Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.

Why puzzle #219 is rated hard

Ratings track how generous the opening is. On #219 you get no region pinned to a single row or column, a smallest color of 3 squares, a tightest row crossed by 2 colors, and a 15-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.

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 hard board from the rest.

When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.

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.

One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #219 the place to look for one is around row 5.

A non-spoiling distribution check: solved, #219 carries 4 queens on the perimeter against 5 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 9x9 Queens puzzle #219?

Puzzle #219 is rated hard. Its smallest color region holds 3 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 9x9 puzzle #219 have only one solution?

Yes. Every puzzle in the 9x9 collection, including #219, 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 #219?

Start with the amber region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 8–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.