9x9 Queens Puzzle #287

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 16-step reasoning is written out below.

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Step-by-step solution for puzzle #287

What follows is a complete solve of puzzle #287, 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 region shadow.

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

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

  1. Step 1. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 7 squares in all.

  2. Step 2. The amber region is down to one open square, at row 2, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 1, the remaining amber squares, and the ring of neighbours around row 2, column 1.

  3. Step 3. Orange cannot leave row 9 — every one of its open squares (2 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 8 squares in all.

  4. Step 4. The khaki region is down to one open square, at row 8, column 8. Every colour holds exactly one queen, so that square is forced. Row 8 and column 8 are now spoken for, along with the squares touching that queen.

    Puzzle #287 after step 4: 2 of 9 queens placed
    The board after step 4 — 2 of 9 queens placed.

  5. Step 5. Slate cannot leave column 9 — every one of its open squares (2 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 3 squares in all.

  6. Step 6. The indigo region is down to one open square, at row 1, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 7, the remaining indigo squares, and the ring of neighbours around row 1, column 7.

  7. Step 7. Wherever red ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

    Puzzle #287 after step 7: 3 of 9 queens placed
    The board after step 7 — 3 of 9 queens placed.

  8. Step 8. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.

  9. Step 9. The blue region has 3 squares left, spread across rows 3 and 5, columns 5 and 6. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.

  10. Step 10. All of the red region's remaining squares (2 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.

  11. Step 11. 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: slate has one square left, so its queen takes row 5, column 9; blue has one square left, so its queen takes row 3, column 6; pale yellow has one square left, so its queen takes row 7, column 5; red has one square left, so its queen takes row 6, column 2; orange has one square left, so its queen takes row 9, column 4; mint has one square left, so its queen takes row 4, 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 4, column 3.

    Puzzle #287 after step 11: 9 of 9 queens placed
    The board after step 11 — 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 #287

9x9 puzzle #287 is rated easy. 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.

There is exactly one way to finish #287, 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 #287 are: orange (2 squares), indigo (3 squares), khaki (4 squares), amber (6 squares), pale yellow (6 squares), slate (8 squares), red (14 squares), mint (17 squares), blue (21 squares). An even split would hand every color 9 squares, so the orange region is running 7 squares under that average while the blue region is the roomiest area on the grid with 21 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Orange has only 2 places to put its queen; blue has 21. The spread between them on this board is 19 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 indigo region is the most compact color here, filling 100% of the 1×3 box that encloses it, while mint is the most scattered at 57% of its 5×6 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.

Orange occupies 2 squares within rows 9–9, columns 4–5. It never leaves row 9, so its queen is locked to that row.

Indigo: 3 squares across rows 1–1, columns 7–9. It never leaves row 1, so its queen is locked to that row.

Khaki covers 4 squares, spanning 2 rows and 3 columns (rows 8–9, columns 7–9).

Amber occupies 6 squares within rows 1–2, columns 1–5.

Pale yellow: 6 squares across rows 7–9, columns 4–6.

Slate covers 8 squares, spanning 4 rows and 3 columns (rows 5–8, columns 7–9).

Red occupies 14 squares within rows 5–9, columns 1–4.

Mint: 17 squares across rows 2–6, columns 1–6.

Blue covers 21 squares, spanning 6 rows and 6 columns (rows 1–6, columns 4–9).

Where to start on this board

Orange is the natural opening on #287: it is the smallest region on the grid at 2 squares, boxed into rows 9–9 and columns 4–5. Since one of those squares must hold a queen, that block of 1 row and 2 columns is the most contested part of the board.

Because orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. 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. Indigo, amber 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 #287

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3 and 4 are the narrowest, touched by only 2 colors. Columns 1, 2, 3 and 6 are the tightest columns, with 3 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 9 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

The middle of #287 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.

With nine queens to seat and nine regions competing over 81 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 9x9 boards quickly and players who stall halfway.

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 #287 is rated easy

Ratings track how generous the opening is. On #287 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 19-square gap between the largest and smallest regions. Those four numbers largely explain the easy 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 easy board from the rest.

Stuck on #287 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.

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 #287 the place to look for one is around row 3.

Use this as a rough check on your progress: the completed board has 4 queens around the border and 5 queens in the middle, and nothing in the 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 #287?

Puzzle #287 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 #287 have only one solution?

Yes. Every puzzle in the 9x9 collection, including #287, 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 #287?

Start with the orange region — the most constrained color on this board, with 2 squares spanning rows 9–9 and columns 4–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.