8x8 Queens Puzzle #149

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 11-step reasoning is written out below.

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Step-by-step solution for puzzle #149

What follows is a complete solve of puzzle #149, worked the way a person works it rather than the way a computer does. It runs to 11 deductions — 8 queen placements and 3 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 confined to one line, region shadow.

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

  1. Step 1. Only row 4, column 1 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 1, the rest of the mint 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. The amber region has 4 squares left, spread across rows 2 and 3, columns 5, 6, and 8. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.

  4. Step 4. The blue region is down to one open square, at row 3, column 3. Every colour holds exactly one queen, so that square is forced. Row 3 and column 3 are now spoken for, along with the squares touching that queen.

    Puzzle #149 after step 4: 2 of 8 queens placed
    The board after step 4 — 2 of 8 queens placed.

  5. Step 5. Only row 1, column 2 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 2, the rest of the indigo region and every square adjacent to it — diagonals included.

  6. Step 6. All of the amber region's remaining squares (3 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.

  7. Step 7. 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: slate has one square left, so its queen takes row 5, column 5; red has one square left, so its queen takes row 6, column 8; amber has one square left, so its queen takes row 2, column 6; khaki has one square left, so its queen takes row 8, column 7; pale yellow has one square left, so its queen takes row 7, column 4. 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 7, column 4.

    Puzzle #149 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 #149

Puzzle #149 is one of the hard-rated boards in the 8x8 set. Eight colors divide its 64 squares, and you win by placing eight queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.

There is exactly one way to finish #149, 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 #149 are: mint (1 square), indigo (4 squares), khaki (5 squares), red (7 squares), amber (8 squares), blue (10 squares), slate (10 squares), pale yellow (19 squares). An even split would hand every color 8 squares, so the mint region is running 7 squares under that average while the pale yellow region is the roomiest area on the grid with 19 squares.

Every color takes one queen and one only, whatever its size — which is why the 18 square difference between mint and pale yellow 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. Mint is the tidiest shape on #149, packing 100% of its 1×1 bounding box, whereas slate straggles across its 4×6 box at just 42%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

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 hard board.

Mint occupies 1 square within rows 4–4, columns 1–1. It never leaves row 4, so its queen is locked to that row.

Indigo: 4 squares across rows 1–2, columns 1–3.

Khaki covers 5 squares, spanning 2 rows and 4 columns (rows 7–8, columns 5–8).

Red occupies 7 squares within rows 4–6, columns 6–8.

Amber: 8 squares across rows 1–3, columns 5–8.

Blue covers 10 squares, spanning 5 rows and 4 columns (rows 1–5, columns 1–4).

Slate occupies 10 squares within rows 2–5, columns 3–8.

Pale yellow: 19 squares across rows 5–8, columns 1–7.

Where to start on this board

Open on the tightest color. Here that is mint, confined to 1 square between rows 4 and 4 and columns 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #149.

Because mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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 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 #149

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 6, 7 and 8 are the narrowest, touched by only 2 colors. Columns 2 and 4 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 5 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

After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.

The whole middle game reduces to two sweeps. Sweep the eight colors looking for one with a single square left; sweep the eight rows and eight columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 8x8 solve from a stalled one.

A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.

Why puzzle #149 is rated hard

The hard label comes out of four measurable things about #149: two 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 18. Boards that score tight on those measures give up their first queen fast.

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.

Stuck on #149 despite the hard 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.

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 #149 is row 6.

Use this as a rough check on your progress: the completed board has 4 queens around the border and 4 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 8x8 Queens puzzle #149?

Puzzle #149 is rated hard. 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 #149 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #149, 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 #149?

Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.