8x8 Queens Puzzle #53

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 8-step reasoning is written out below.

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Step-by-step solution for puzzle #53

What follows is a complete solve of puzzle #53, worked the way a person works it rather than the way a computer does. It runs to 8 deductions, every one of them a forced placement. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the last square in a region.

Techniques this board needs: last square in a region.

Show the full walkthrough (8 steps) — contains the solution

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

  2. Step 2. The indigo region is down to one open square, at row 1, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 3, the remaining indigo squares, and the ring of neighbours around row 1, column 3.

  3. Step 3. Only row 5, column 7 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 7, in slate and in the ring around that square is now dead.

  4. Step 4. The blue region is down to one open square, at row 3, column 8. Every colour holds exactly one queen, so that square is forced. Row 3 and column 8 are now spoken for, along with the squares touching that queen.

    Puzzle #53 after step 4: 4 of 8 queens placed
    The board after step 4 — 4 of 8 queens placed.

  5. Step 5. 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.

  6. Step 6. The mint region is down to one open square, at row 4, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 4, the remaining mint squares, and the ring of neighbours around row 4, column 4.

  7. Step 7. Only row 8, column 6 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 6, in khaki and in the ring around that square is now dead.

  8. Step 8. The pale yellow region is down to one open square, at row 7, column 2. Every colour holds exactly one queen, so that square is forced. Row 7 and column 2 are now spoken for, along with the squares touching that queen.

    Puzzle #53 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 #53

Puzzle #53 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 #53, 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 #53 are: amber (1 square), slate (1 square), blue (5 squares), indigo (7 squares), red (9 squares), khaki (9 squares), pale yellow (13 squares), mint (19 squares). An even split would hand every color 8 squares, so the amber region is running 7 squares under that average while the mint region is the roomiest area on the grid with 19 squares.

Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So amber, with 1 square, is under far more pressure than mint with 19. A 18-square gap like this one rewards players who start where the choices are fewest.

Square count is only half the story — how a color is arranged counts too. Amber is the tidiest shape on #53, packing 100% of its 1×1 bounding box, whereas red straggles across its 3×6 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Below is every color on #53 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.

Amber occupies 1 square within rows 2–2, columns 1–1. It never leaves row 2, so its queen is locked to that row.

Slate: 1 square across rows 5–5, columns 7–7. It never leaves row 5, so its queen is locked to that row.

Blue covers 5 squares, spanning 5 rows and 1 column (rows 1–5, columns 8–8). It sits wholly inside column 8, so its queen must be in that column.

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

Red: 9 squares across rows 5–7, columns 3–8.

Khaki covers 9 squares, spanning 2 rows and 6 columns (rows 7–8, columns 3–8).

Pale yellow occupies 13 squares within rows 4–8, columns 1–4.

Mint: 19 squares across rows 1–5, columns 3–7.

Where to start on this board

Open on the tightest color. Here that is amber, confined to 1 square between rows 2 and 2 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 #53.

Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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 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 #53

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 6 and 8 are the narrowest, touched by only 2 colors. Column 2 is the tightest column, with 2 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 5 colors crossing it; it will almost certainly be among the last to settle.

Working through the middle game

Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.

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 #53 is rated medium

What earns a board its rating is the shape of its opening. Here that opening offers five single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 18. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

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 #53 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.

Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #53, start hunting for it near 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 #53?

Puzzle #53 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.

Does 8x8 puzzle #53 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #53, 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 #53?

Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.