8x8 Queens Puzzle #108

Difficulty: medium. Place 8 queens on this 8x8 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 12-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 12 deductions — 8 queen placements and 4 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: last square in a region, region shadow, region confined to one line.

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

  1. Step 1. Only row 3, column 1 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 1, the rest of the blue region and every square adjacent to it — diagonals included.

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

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

  4. Step 4. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.

    Puzzle #108 after step 4: 1 of 8 queens placed
    The board after step 4 — 1 of 8 queens placed.

  5. Step 5. Only row 4, column 3 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 3, the rest of the mint region and every square adjacent to it — diagonals included.

  6. Step 6. The khaki region is down to one open square, at row 8, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 2, the remaining khaki squares, and the ring of neighbours around row 8, column 2.

  7. Step 7. Red cannot leave column 4 — every one of its open squares (2 open squares) sits there. That column belongs to red, 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 5 queens fall out in order without any new idea being needed: amber has one square left, so its queen takes row 2, column 5; indigo has one square left, so its queen takes row 1, column 7; pale yellow has one square left, so its queen takes row 7, column 6; red has one square left, so its queen takes row 6, column 4; slate has one square left, so its queen takes row 5, 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 5, column 8.

    Puzzle #108 after step 8: 8 of 8 queens placed
    The board after step 8 — 8 of 8 queens placed.

That completes the board: 8 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 8x8 Queens puzzle #108

This is puzzle number 108 in the 8x8 collection, rated medium. The grid holds 64 squares split between eight colored regions, and a finished board carries eight 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: blue (1 square), pale yellow (3 squares), indigo (4 squares), khaki (6 squares), amber (8 squares), red (10 squares), mint (11 squares), slate (21 squares). An even split would hand every color 8 squares, so the blue region is running 7 squares under that average while the slate region is the roomiest area on the grid with 21 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 blue, with 1 square, is under far more pressure than slate with 21. A 20-square gap like this one rewards players who start where the choices are fewest.

Shape matters as much as size. The blue region is the most compact color here, filling 100% of the 1×1 box that encloses it, while slate is the most scattered at 53% of its 8×5 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.

Blue: 1 square across rows 3–3, columns 1–1. It never leaves row 3, so its queen is locked to that row.

Pale yellow covers 3 squares, spanning 2 rows and 2 columns (rows 7–8, columns 5–6).

Indigo occupies 4 squares within rows 1–2, columns 5–7.

Khaki: 6 squares across rows 5–8, columns 1–2.

Amber covers 8 squares, spanning 2 rows and 5 columns (rows 2–3, columns 3–7).

Red occupies 10 squares within rows 5–8, columns 2–5.

Mint: 11 squares across rows 1–4, columns 1–4.

Slate covers 21 squares, spanning 8 rows and 5 columns (rows 1–8, columns 4–8).

Where to start on this board

The most constrained color is where a solve should begin, and on #108 that is blue with 1 square. It reaches from row 3 to row 3 and from column 1 to column 1 — 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 blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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 pale yellow 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 #108

A quick way to find the next move is to count how many different colors touch each line. On this board, row 4 is the narrowest, touched by only 2 colors. Column 8 is the tightest column, with 1 color.

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 7 rows. Row 8, meeting 4 colors, is the opposite case — the busiest line on #108 and the last one you should expect to crack.

Working through the middle game

The middle of #108 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.

Two checks, run alternately, will carry you through the 64 squares of this grid. First: has any of the eight regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 8x8 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 medium

Ratings track how generous the opening is. On #108 you get two regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 20-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.

Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.

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 8x8

At 8x8 the whole grid stays within a single glance, which makes systematic scanning practical. Read the rows in order and count the colors in each — a row touched by two colors is far more constrained than one touched by five, and that is usually where the next forced move hides. The board is small enough that re-scanning from the top after each placement costs almost nothing.

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 #108, start hunting for it near column 8.

Here is a shape check that gives nothing away: when #108 is solved, 4 queens sit on the outer edge of the grid and 4 sit inside it, and no queen lands 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 8x8 Queens puzzle #108?

Puzzle #108 is rated medium. Its smallest color region holds 1 square, 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 8x8 puzzle #108 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #108, has been verified to have exactly one valid arrangement of eight 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 blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.