9x9 Queens Puzzle #108

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 20-step reasoning is written out below.

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Step-by-step solution for puzzle #108

What follows is a complete solve of puzzle #108, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 9 queen placements and 11 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 rows.

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

Show the full walkthrough (14 steps) — contains the solution

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

  2. Step 2. Amber is down to 3 candidates in rows 1 and 2, columns 2 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.

  3. Step 3. Red cannot leave column 9 — every one of its open squares (4 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 4 squares in all.

  4. Step 4. Wherever pale yellow ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

  5. Step 5. Orange is down to 5 candidates in rows 7–9, columns 2–4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about orange itself.

    Puzzle #108 after step 5: 1 of 9 queens placed
    The board after step 5 — 1 of 9 queens placed.

  6. Step 6. Here is the pairing argument. The red, pale yellow, khaki, and orange regions have no open squares outside rows 6–9 — 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: 8 squares come off in one stroke.

  7. Step 7. 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.

  8. Step 8. Blue is down to 3 candidates in rows 2 and 3, columns 3, 4, and 6, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about blue itself.

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

    Puzzle #108 after step 9: 2 of 9 queens placed
    The board after step 9 — 2 of 9 queens placed.

  10. Step 10. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.

  11. Step 11. 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: 1 square in all.

  12. Step 12. All of the khaki region's remaining squares (2 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.

  13. Step 13. Row 3 has only blue squares left (2 open squares). The row needs a queen and only blue can provide one, which pins that colour to this row and kills its squares elsewhere: 1 square.

  14. Step 14. 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: column 6 is down to one square, putting a queen on row 1, column 6; amber has one square left, so its queen takes row 2, column 2; blue has one square left, so its queen takes row 3, column 4; orange has one square left, so its queen takes row 9, column 3; 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 9; khaki has one square left, so its queen takes row 8, column 8. 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 8.

    Puzzle #108 after step 14: 9 of 9 queens placed
    The board after step 14 — 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 #108

This is puzzle number 108 in the 9x9 collection, rated easy. The grid holds 81 squares split between nine colored regions, and a finished board carries nine queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.

Puzzle #108 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 #108 are: slate (1 square), red (5 squares), amber (7 squares), khaki (7 squares), pale yellow (8 squares), blue (11 squares), orange (11 squares), mint (13 squares), indigo (18 squares). An even split would hand every color 9 squares, so the slate region is running 8 squares under that average while the indigo region is the roomiest area on the grid with 18 squares.

Every color takes one queen and one only, whatever its size — which is why the 17 square difference between slate and indigo 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.

Square count is only half the story — how a color is arranged counts too. Slate is the tidiest shape on #108, packing 100% of its 1×1 bounding box, whereas blue straggles across its 4×5 box at just 55%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Here is the full footprint of every color on puzzle #108, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

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

Red covers 5 squares, spanning 5 rows and 1 column (rows 5–9, columns 9–9). It sits wholly inside column 9, so its queen must be in that column.

Amber occupies 7 squares within rows 1–4, columns 1–3.

Khaki: 7 squares across rows 7–9, columns 5–8.

Pale yellow covers 8 squares, spanning 4 rows and 3 columns (rows 5–8, columns 3–5).

Blue occupies 11 squares within rows 2–5, columns 2–6.

Orange: 11 squares across rows 6–9, columns 1–4.

Mint covers 13 squares, spanning 5 rows and 4 columns (rows 4–8, columns 5–8).

Indigo occupies 18 squares within rows 1–4, columns 3–9.

Where to start on this board

Begin where the choices are fewest. On this board that means slate, which owns just 1 square inside a 1×1 window running from row 5 to row 5 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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.

Nothing on this grid is pinned to one or two lines, which is why the opening takes patience. Scan the columns for one where only two or three colors appear — whichever region is forced into it claims that column outright. Chaining two of those observations is normally enough to break #108 open.

The tightest lines on puzzle #108

A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Column 9 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 8 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

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 #108 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 #108 is rated easy

The rating reflects how much the board concedes up front. Puzzle #108 has three 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 17 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.

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.

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 #108 is row 1.

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 #108?

Puzzle #108 is rated easy. Its smallest color region holds 1 square, 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 #108 have only one solution?

Yes. Every puzzle in the 9x9 collection, including #108, 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 #108?

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