8x8 Queens Puzzle #192

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 13-step reasoning is written out below.

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Step-by-step solution for puzzle #192

What follows is a complete solve of puzzle #192, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 8 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: 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 8, column 3 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 3, the rest of the khaki region and every square adjacent to it — diagonals included.

  2. Step 2. Amber is down to 4 candidates in rows 1 and 2, columns 6–8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.

  3. Step 3. Blue cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 7 squares in all.

  4. Step 4. The red region is down to one open square, at row 6, column 2. Every colour holds exactly one queen, so that square is forced. Row 6 and column 2 are now spoken for, along with the squares touching that queen.

    Puzzle #192 after step 4: 2 of 8 queens placed
    The board after step 4 — 2 of 8 queens placed.

  5. Step 5. Indigo is down to 3 candidates in rows 1 and 2, columns 4 and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.

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

  7. Step 7. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 2 squares in all.

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

    Puzzle #192 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 #192

This is puzzle number 192 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.

There is exactly one way to finish #192, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these eight regions is what sets the depth.

How the colors divide this board

From smallest to largest, the regions on puzzle #192 are: khaki (1 square), blue (2 squares), amber (4 squares), indigo (7 squares), pale yellow (7 squares), red (9 squares), slate (11 squares), mint (23 squares). An even split would hand every color 8 squares, so the khaki region is running 7 squares under that average while the mint region is the roomiest area on the grid with 23 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Khaki is working with 1 square while mint has 23 to spare, a gap of 22. Attack the cramped end and the roomy regions tend to resolve themselves.

Shape matters as much as size. The blue region is the most compact color here, filling 100% of the 2×1 box that encloses it, while slate is the most scattered at 44% of its 5×5 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

Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a medium board.

Khaki: 1 square across rows 8–8, columns 3–3. It never leaves row 8, so its queen is locked to that row.

Blue covers 2 squares, spanning 2 rows and 1 column (rows 2–3, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.

Amber occupies 4 squares within rows 1–2, columns 6–8.

Indigo: 7 squares across rows 1–2, columns 1–5.

Pale yellow covers 7 squares, spanning 3 rows and 4 columns (rows 6–8, columns 5–8).

Red occupies 9 squares within rows 5–8, columns 1–3.

Slate: 11 squares across rows 4–8, columns 1–5.

Mint covers 23 squares, spanning 6 rows and 7 columns (rows 2–7, columns 2–8).

Where to start on this board

The most constrained color is where a solve should begin, and on #192 that is khaki with 1 square. It reaches from row 8 to row 8 and from column 3 to column 3 — 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 khaki never leaves row 8, its queen must be in that row — and that instantly settles row 8 for everyone else. Sweep along it and X out every square that is not khaki. 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 blue 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 #192

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3 and 4 are the narrowest, touched by only 2 colors. Columns 4, 6, 7 and 8 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 7 rows. Row 8 is the crowded extreme at 4 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.

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 #192 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 #192 is rated medium

The medium label comes out of four measurable things about #192: three of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 22. Boards that score tight on those measures give up their first queen fast.

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 medium board from the rest.

Stuck on #192 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.

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.

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.

A non-spoiling distribution check: solved, #192 carries 4 queens on the perimeter against 4 queens inside, with the corners empty. 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 8x8 Queens puzzle #192?

Puzzle #192 is rated medium. 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 8x8 puzzle #192 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #192, 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 #192?

Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.