8x8 Queens Puzzle #145

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 11-step reasoning is written out below.

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Step-by-step solution for puzzle #145

What follows is a complete solve of puzzle #145, 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 shadow, region confined to one line.

Show the full walkthrough (6 steps) — contains the solution

  1. Step 1. Only row 4, column 8 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 8, the rest of the mint region and every square adjacent to it — diagonals included.

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

  3. Step 3. The blue region has 4 squares left, spread across rows 3, 5, and 6, columns 3–5. 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.

    Puzzle #145 after step 3: 2 of 8 queens placed
    The board after step 3 — 2 of 8 queens placed.

  4. Step 4. All of the slate region's remaining squares (2 open squares) lie in row 5. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.

  5. Step 5. Red cannot leave row 6 — every one of its open squares (2 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 4 squares in all.

  6. Step 6. 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: khaki has one square left, so its queen takes row 8, column 6; red has one square left, so its queen takes row 6, column 5; blue has one square left, so its queen takes row 3, column 3; slate has one square left, so its queen takes row 5, column 2; pale yellow has one square left, so its queen takes row 7, column 1; indigo has one square left, so its queen takes row 1, 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 1, column 4.

    Puzzle #145 after step 6: 8 of 8 queens placed
    The board after step 6 — 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 #145

Puzzle #145 is one of the medium-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 #145, 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 #145 are: mint (1 square), slate (4 squares), amber (5 squares), khaki (6 squares), red (8 squares), blue (12 squares), indigo (14 squares), pale yellow (14 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 14 squares.

Every color takes one queen and one only, whatever its size — which is why the 13 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 #145, packing 100% of its 1×1 bounding box, whereas blue straggles across its 5×5 box at just 48%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

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.

Mint covers 1 square, spanning 1 row and 1 column (rows 4–4, columns 8–8). It never leaves row 4, so its queen is locked to that row.

Slate occupies 4 squares within rows 4–5, columns 1–3.

Amber: 5 squares across rows 1–3, columns 7–8.

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

Red occupies 8 squares within rows 5–6, columns 5–8.

Blue: 12 squares across rows 2–6, columns 3–7.

Indigo covers 14 squares, spanning 3 rows and 7 columns (rows 1–3, columns 1–7).

Pale yellow occupies 14 squares within rows 5–8, columns 1–5.

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 8 and 8. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #145.

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. Slate, red 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 #145

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

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 5, meeting 4 colors, is the opposite case — the busiest line on #145 and the last one you should expect to crack.

Working through the middle game

The middle of #145 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.

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 #145 is rated medium

Ratings track how generous the opening is. On #145 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 13-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.

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 #145 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.

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 #145 is row 1.

Here is a shape check that gives nothing away: when #145 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 #145?

Puzzle #145 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 #145 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #145, 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 #145?

Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.