9x9 Queens Puzzle #249

Difficulty: medium. 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 9-step reasoning is written out below.

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Step-by-step solution for puzzle #249

What follows is a complete solve of puzzle #249, worked the way a person works it rather than the way a computer does. It runs to 9 deductions, every one of them a forced placement. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the last square in a row.

Techniques this board needs: last square in a region, last square in a row.

Show the full walkthrough (9 steps) — contains the solution

  1. Step 1. Only row 6, column 5 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 5, the rest of the red region and every square adjacent to it — diagonals included.

  2. Step 2. The orange region is down to one open square, at row 9, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 7, the remaining orange squares, and the ring of neighbours around row 9, column 7.

  3. Step 3. Only row 8, column 2 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 2, in khaki and in the ring around that square is now dead.

    Puzzle #249 after step 3: 3 of 9 queens placed
    The board after step 3 — 3 of 9 queens placed.

  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.

  5. Step 5. Only row 2, column 8 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 8, the rest of the amber region and every square adjacent to it — diagonals included.

  6. Step 6. Row 7 has a single open square left, at column 9 in the pale yellow region. Every row needs a queen, so this one is forced. Row 7 and column 9 are now spoken for, along with the squares touching that queen.

    Puzzle #249 after step 6: 6 of 9 queens placed
    The board after step 6 — 6 of 9 queens placed.

  7. Step 7. Only row 4, column 6 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 6, in mint and in the ring around that square is now dead.

  8. Step 8. 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. Row 5 and column 3 are now spoken for, along with the squares touching that queen.

  9. Step 9. Only row 3, column 4 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 4, the rest of the blue region and every square adjacent to it — diagonals included.

    Puzzle #249 after step 9: 9 of 9 queens placed
    The board after step 9 — 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 #249

Puzzle #249 is one of the medium-rated boards in the 9x9 set. Nine colors divide its 81 squares, and you win by placing nine queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.

As with every puzzle in this collection, #249 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.

How the colors divide this board

From smallest to largest, the regions on puzzle #249 are: red (1 square), orange (1 square), indigo (2 squares), amber (4 squares), khaki (4 squares), mint (10 squares), blue (16 squares), slate (21 squares), pale yellow (22 squares). An even split would hand every color 9 squares, so the red region is running 8 squares under that average while the pale yellow 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 21 square difference between red 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.

A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×2 box, and mint the most diffuse at 50% of its 4×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

Here is the full footprint of every color on puzzle #249, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Red: 1 square across rows 6–6, columns 5–5. It never leaves row 6, so its queen is locked to that row.

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

Indigo occupies 2 squares within rows 1–1, columns 1–2. It never leaves row 1, so its queen is locked to that row.

Amber: 4 squares across rows 1–2, columns 7–9.

Khaki covers 4 squares, spanning 2 rows and 3 columns (rows 8–9, columns 1–3).

Mint occupies 10 squares within rows 2–5, columns 5–9.

Blue: 16 squares across rows 1–5, columns 2–6.

Slate covers 21 squares, spanning 7 rows and 5 columns (rows 2–8, columns 1–5).

Pale yellow occupies 22 squares within rows 4–9, columns 4–9.

Where to start on this board

The most constrained color is where a solve should begin, and on #249 that is red with 1 square. It reaches from row 6 to row 6 and from column 5 to column 5 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.

Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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, orange, 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 #249

A quick way to find the next move is to count how many different colors touch each line. On this board, row 7 is the narrowest, touched by only 2 colors. Columns 1, 3, 4, 6, 8 and 9 are the tightest columns, with 3 colors.

The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 8 rows. Row 5, meeting 4 colors, is the opposite case — the busiest line on #249 and the last one you should expect to crack.

Working through the middle game

Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.

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.

Resist the plausible-looking queen. On #249 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.

Why puzzle #249 is rated medium

The rating reflects how much the board concedes up front. Puzzle #249 has five regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 21 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.

A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.

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 #249 is row 7.

Here is a shape check that gives nothing away: when #249 is solved, 3 queens sit on the outer edge of the grid and 6 sit inside it, with 1 queen in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.

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 #249?

Puzzle #249 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.

Does 9x9 puzzle #249 have only one solution?

Yes. Every puzzle in the 9x9 collection, including #249, 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 #249?

Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.