8x8 Queens Puzzle #148

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 10-step reasoning is written out below.

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Step-by-step solution for puzzle #148

What follows is a complete solve of puzzle #148, 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 shadow.

Techniques this board needs: last square in a region, region shadow.

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

  1. Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: slate has one square left, so its queen takes row 5, column 3; mint has one square left, so its queen takes row 4, column 8; blue has one square left, so its queen takes row 3, column 2; indigo has one square left, so its queen takes row 1, column 1. 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 1, column 1.

  2. Step 2. Red is down to 3 candidates in rows 6 and 7, columns 5 and 6, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about red itself.

  3. Step 3. The khaki region is down to one open square, at row 8, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 4, the remaining khaki squares, and the ring of neighbours around row 8, column 4.

  4. Step 4. Wherever red ends up among its 2 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

    Puzzle #148 after step 4: 5 of 8 queens placed
    The board after step 4 — 5 of 8 queens placed.

  5. Step 5. The pale yellow region is down to one open square, at row 7, column 7. Every colour holds exactly one queen, so that square is forced. Row 7 and column 7 are now spoken for, along with the squares touching that queen.

  6. Step 6. Only row 6, column 5 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 5, the rest of the red region and every square adjacent to it — diagonals included.

  7. Step 7. The amber region is down to one open square, at row 2, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 6, the remaining amber squares, and the ring of neighbours around row 2, column 6.

    Puzzle #148 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 #148

This is puzzle number 148 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 #148 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 #148 are: slate (1 square), khaki (2 squares), mint (3 squares), blue (6 squares), indigo (7 squares), pale yellow (9 squares), amber (14 squares), red (22 squares). An even split would hand every color 8 squares, so the slate region is running 7 squares under that average while the red region is the roomiest area on the grid with 22 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Slate is working with 1 square while red has 22 to spare, a gap of 21. Attack the cramped end and the roomy regions tend to resolve themselves.

Square count is only half the story — how a color is arranged counts too. Slate is the tidiest shape on #148, packing 100% of its 1×1 bounding box, whereas red straggles across its 6×8 box at just 46%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Below is every color on #148 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.

Slate covers 1 square, spanning 1 row and 1 column (rows 5–5, columns 3–3). It never leaves row 5, so its queen is locked to that row.

Khaki occupies 2 squares within rows 7–8, columns 4–4. It sits wholly inside column 4, so its queen must be in that column.

Mint: 3 squares across rows 4–5, columns 7–8.

Blue covers 6 squares, spanning 2 rows and 4 columns (rows 3–4, columns 1–4).

Indigo occupies 7 squares within rows 1–3, columns 1–3.

Pale yellow: 9 squares across rows 6–8, columns 5–8.

Amber covers 14 squares, spanning 4 rows and 5 columns (rows 1–4, columns 4–8).

Red occupies 22 squares within rows 3–8, columns 1–8.

Where to start on this board

The most constrained color is where a solve should begin, and on #148 that is slate with 1 square. It reaches from row 5 to row 5 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 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.

Work outward to the other flat regions next. Blue, mint and khaki 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 #148

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2 and 6 are the narrowest, touched by only 2 colors. Columns 1, 2, 5 and 6 are the tightest columns, with 3 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 7 rows. Row 4 sits at the far end with 4 colors crossing it; it will almost certainly be among the last to settle.

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.

With eight queens to seat and eight regions competing over 64 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 8x8 boards quickly and players who stall halfway.

Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.

Why puzzle #148 is rated medium

What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 21. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

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 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.

Use this as a rough check on your progress: the completed board has 3 queens around the border and 5 queens in the middle, including 1 in a corner. 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 8x8 Queens puzzle #148?

Puzzle #148 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 #148 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #148, 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 #148?

Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.