9x9 Queens Puzzle #42

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 14-step reasoning is written out below.

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Step-by-step solution for puzzle #42

What follows is a complete solve of puzzle #42, 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 pairing argument on columns.

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

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

  1. Step 1. Only row 1, column 8 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 8, the rest of the indigo 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 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 1, the remaining orange squares, and the ring of neighbours around row 9, column 1.

  3. Step 3. The amber region has 7 squares left, spread across rows 2–5, columns 4–6. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.

  4. Step 4. Wherever slate 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.

    Puzzle #42 after step 4: 2 of 9 queens placed
    The board after step 4 — 2 of 9 queens placed.

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

  6. Step 6. Here is the pairing argument. The slate, red, pale yellow, and khaki regions have no open squares outside rows 5–8 — 4 colours confined to 4 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 5 squares come off in one stroke.

  7. Step 7. Blue and slate are now boxed into columns 6 and 7 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 7 queens fall out in order without any new idea being needed: khaki has one square left, so its queen takes row 8, column 4; pale yellow has one square left, so its queen takes row 7, column 2; red has one square left, so its queen takes row 6, column 9; slate has one square left, so its queen takes row 5, column 6; amber has one square left, so its queen takes row 2, column 5; blue has one square left, so its queen takes row 3, column 7; 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 #42 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 #42

Board #42 of the 9x9 bank carries a easy rating. Its 81 squares are shared between nine colored regions, and the solution places nine queens: one per row, one per column, one per region, none of them side by side or corner to corner.

As with every puzzle in this collection, #42 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 #42 are: indigo (1 square), orange (1 square), slate (3 squares), blue (10 squares), red (10 squares), pale yellow (11 squares), khaki (13 squares), amber (15 squares), mint (17 squares). An even split would hand every color 9 squares, so the indigo region is running 8 squares under that average while the mint region is the roomiest area on the grid with 17 squares.

Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So indigo, with 1 square, is under far more pressure than mint with 17. A 16-square gap like this one rewards players who start where the choices are fewest.

Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×1 box that encloses it, while amber is the most scattered at 50% 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

Below is every color on #42 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.

Indigo: 1 square across rows 1–1, columns 8–8. It never leaves row 1, so its queen is locked to that row.

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

Slate occupies 3 squares within rows 5–6, columns 6–7.

Blue: 10 squares across rows 3–5, columns 5–9.

Red covers 10 squares, spanning 5 rows and 3 columns (rows 5–9, columns 7–9).

Pale yellow occupies 11 squares within rows 5–8, columns 1–5.

Khaki: 13 squares across rows 7–9, columns 1–7.

Amber covers 15 squares, spanning 5 rows and 6 columns (rows 1–5, columns 4–9).

Mint occupies 17 squares within rows 1–6, columns 1–3.

Where to start on this board

Open on the tightest color. Here that is indigo, confined to 1 square between rows 1 and 1 and columns 8 and 8. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #42.

Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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 and slate 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 #42

A quick way to find the next move is to count how many different colors touch each line. On this board, row 2 is the narrowest, touched by only 2 colors. Columns 2, 3, 4 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 5 is the crowded extreme at 6 colors — worth revisiting later, not now.

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.

The whole middle game reduces to two sweeps. Sweep the nine colors looking for one with a single square left; sweep the nine rows and nine columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 9x9 solve from a stalled one.

A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.

Why puzzle #42 is rated easy

What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 16. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

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.

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.

Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #42, start hunting for it near row 2.

A non-spoiling distribution check: solved, #42 carries 3 queens on the perimeter against 6 queens inside, 1 of them cornered. 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 #42?

Puzzle #42 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.

Does 9x9 puzzle #42 have only one solution?

Yes. Every puzzle in the 9x9 collection, including #42, 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 #42?

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