8x8 Queens Puzzle #102

Difficulty: hard. 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 10-step reasoning is written out below.

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Step-by-step solution for puzzle #102

What follows is a complete solve of puzzle #102, worked the way a person works it rather than the way a computer does. It runs to 10 deductions — 8 queen placements and 2 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 confined to one line.

Techniques this board needs: last square in a region, region confined to one line, last square in a column.

Show the full walkthrough (7 steps) — contains the solution

  1. Step 1. Only row 7, column 8 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 8, the rest of the pale yellow region and every square adjacent to it — diagonals included.

  2. Step 2. 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: 7 squares come off.

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

  4. Step 4. The indigo region is down to one open square, at row 1, column 6. Every colour holds exactly one queen, so that square is forced. Row 1 and column 6 are now spoken for, along with the squares touching that queen.

    Puzzle #102 after step 4: 3 of 8 queens placed
    The board after step 4 — 3 of 8 queens placed.

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

  6. Step 6. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.

  7. Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: column 4 is down to one square, putting a queen on row 8, column 4; red has one square left, so its queen takes row 6, column 1; amber has one square left, so its queen takes row 2, column 2; 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 #102 after step 7: 8 of 8 queens placed
    The board after step 7 — 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 #102

Board #102 of the 8x8 bank carries a hard rating. Its 64 squares are shared between eight colored regions, and the solution places eight queens: one per row, one per column, one per region, none of them side by side or corner to corner.

Puzzle #102 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 #102 are: pale yellow (1 square), indigo (3 squares), red (4 squares), blue (6 squares), amber (8 squares), slate (9 squares), khaki (15 squares), mint (18 squares). An even split would hand every color 8 squares, so the pale yellow region is running 7 squares under that average while the mint region is the roomiest area on the grid with 18 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Pale yellow has only 1 place to put its queen; mint has 18. The spread between them on this board is 17 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×3 frame; mint is the loosest, occupying only 50% of its 6×6 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

Region by region

Here is the full footprint of every color on puzzle #102, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Pale yellow: 1 square across rows 7–7, columns 8–8. It never leaves row 7, so its queen is locked to that row.

Indigo covers 3 squares, spanning 1 row and 3 columns (rows 1–1, columns 6–8). It never leaves row 1, so its queen is locked to that row.

Red occupies 4 squares within rows 5–8, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.

Blue: 6 squares across rows 2–5, columns 7–8.

Amber covers 8 squares, spanning 3 rows and 3 columns (rows 1–3, columns 1–3).

Slate occupies 9 squares within rows 4–7, columns 5–8.

Khaki: 15 squares across rows 6–8, columns 2–8.

Mint covers 18 squares, spanning 6 rows and 6 columns (rows 1–6, columns 1–6).

Where to start on this board

Pale yellow is the natural opening on #102: it is the smallest region on the grid at 1 square, boxed into rows 7–7 and columns 8–8. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.

Because pale yellow never leaves row 7, its queen must be in that row — and that instantly settles row 7 for everyone else. Sweep along it and X out every square that is not pale yellow. 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 is no more than two rows tall, so its queen is 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 #102

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

Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 7 rows. By contrast row 7 meets 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.

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.

Keep alternating between two views of the board. In the region view you ask which of the eight colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 8x8 board unwinds.

The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.

Why puzzle #102 is rated hard

The rating reflects how much the board concedes up front. Puzzle #102 has four 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.

Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.

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.

One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #102 the place to look for one is around row 8.

As a sanity check rather than a spoiler: the finished solution to #102 puts 4 queens on the outer border and 4 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.

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 #102?

Puzzle #102 is rated hard. 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 8x8 puzzle #102 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #102, 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 #102?

Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.