9x9 Queens Puzzle #139

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 14-step reasoning is written out below.

Previous puzzle · All 9x9 puzzles · Next puzzle

Step-by-step solution for puzzle #139

What follows is a complete solve of puzzle #139, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 9 queen placements and 5 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 (8 steps) — contains the solution

  1. Step 1. Mint cannot leave column 7 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 11 squares in all.

  2. Step 2. The slate region is down to one open square, at row 5, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 9, the remaining slate squares, and the ring of neighbours around row 5, column 9.

  3. Step 3. Only row 4, column 7 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 7, in mint and in the ring around that square is now dead.

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

    Puzzle #139 after step 4: 2 of 9 queens placed
    The board after step 4 — 2 of 9 queens placed.

  5. Step 5. Red cannot leave row 6 — every one of its open squares (2 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 6 squares in all.

  6. Step 6. All of the blue region's remaining squares (3 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.

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

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

    Puzzle #139 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 #139

9x9 puzzle #139 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 #139 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 #139 are: mint (2 squares), slate (2 squares), red (4 squares), orange (4 squares), pale yellow (7 squares), indigo (12 squares), amber (12 squares), blue (13 squares), khaki (25 squares). An even split would hand every color 9 squares, so the mint region is running 7 squares under that average while the khaki region is the roomiest area on the grid with 25 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Mint is working with 2 squares while khaki has 25 to spare, a gap of 23. Attack the cramped end and the roomy regions tend to resolve themselves.

Shape matters as much as size. The mint region is the most compact color here, filling 100% of the 2×1 box that encloses it, while blue is the most scattered at 65% of its 4×5 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.

Mint covers 2 squares, spanning 2 rows and 1 column (rows 4–5, columns 7–7). It sits wholly inside column 7, so its queen must be in that column.

Slate occupies 2 squares within rows 5–5, columns 8–9. It never leaves row 5, so its queen is locked to that row.

Red: 4 squares across rows 5–6, columns 2–3.

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

Pale yellow occupies 7 squares within rows 3–9, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.

Indigo: 12 squares across rows 1–3, columns 1–6.

Amber covers 12 squares, spanning 4 rows and 4 columns (rows 1–4, columns 6–9).

Blue occupies 13 squares within rows 3–6, columns 2–6.

Khaki: 25 squares across rows 6–9, columns 3–9.

Where to start on this board

Mint is the natural opening on #139: it is the smallest region on the grid at 2 squares, boxed into rows 4–5 and columns 7–7. Since one of those squares must hold a queen, that block of 2 rows and 1 column is the most contested part of the board.

Because mint stays inside column 7, its queen belongs to that column and no other region may use it. Cross out the rest of column 7 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.

Work outward to the other flat regions next. Slate and red 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 #139

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 2 are 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 5 sits at the far end with 5 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.

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 #139 is rated hard

Ratings track how generous the opening is. On #139 you get three regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 23-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.

Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 1 on this board.

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.

Full rules · Strategy library · Puzzle statistics

Questions about this puzzle

How hard is 9x9 Queens puzzle #139?

Puzzle #139 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.

Does 9x9 puzzle #139 have only one solution?

Yes. Every puzzle in the 9x9 collection, including #139, 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 #139?

Start with the mint region — the most constrained color on this board, with 2 squares spanning rows 4–5 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.