8x8 Queens Puzzle #93

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 12-step reasoning is written out below.

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Step-by-step solution for puzzle #93

What follows is a complete solve of puzzle #93, worked the way a person works it rather than the way a computer does. It runs to 12 deductions — 8 queen placements and 4 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 pairing argument on rows.

Techniques this board needs: region shadow, region confined to one line, pairing argument on rows, last square in a region, last square in a column.

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

  1. Step 1. Wherever mint ends up among its 3 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.

  2. Step 2. All of the indigo region's remaining squares (3 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.

  3. Step 3. Amber, blue, and mint are now boxed into rows 2–4 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 10 squares at once.

    Puzzle #93 after step 3: 0 of 8 queens placed
    The board after step 3 — 0 of 8 queens placed.

  4. Step 4. The slate region is down to one open square, at row 5, column 1. Every colour holds exactly one queen, so that square is forced. Row 5 and column 1 are now spoken for, along with the squares touching that queen.

  5. Step 5. 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: 8 squares in all.

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

    Puzzle #93 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 #93

Puzzle #93 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 #93, 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 #93 are: mint (3 squares), indigo (4 squares), blue (5 squares), slate (6 squares), pale yellow (7 squares), amber (9 squares), khaki (9 squares), red (21 squares). An even split would hand every color 8 squares, so the mint region is running 5 squares under that average while the red region is the roomiest area on the grid with 21 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 mint, with 3 squares, is under far more pressure than red with 21. 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. Blue is the tidiest shape on #93, packing 83% of its 3×2 bounding box, whereas amber straggles across its 4×5 box at just 45%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Below is every color on #93 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.

Mint: 3 squares across rows 3–4, columns 5–6.

Indigo covers 4 squares, spanning 2 rows and 3 columns (rows 1–2, columns 5–7).

Blue occupies 5 squares within rows 1–3, columns 7–8.

Slate: 6 squares across rows 2–5, columns 1–2.

Pale yellow covers 7 squares, spanning 4 rows and 3 columns (rows 5–8, columns 1–3).

Amber occupies 9 squares within rows 1–4, columns 1–5.

Khaki: 9 squares across rows 4–8, columns 6–8.

Red covers 21 squares, spanning 6 rows and 6 columns (rows 3–8, columns 2–7).

Where to start on this board

Open on the tightest color. Here that is mint, confined to 3 squares between rows 3 and 4 and columns 5 and 6. Its queen has nowhere else to go, which means those 2 rows and 2 columns carry more constraint than anywhere else on #93.

Mint does not collapse onto a single line, so it will not hand you a queen on move one. What it does give you is a short list of 3 candidates. Take each one in turn, imagine the queen there, cross out its row, its column and the eight squares around it, and ask whether any other region is left with nowhere to go. One or two candidates usually fail that test immediately.

Work outward to the other flat regions next. Indigo is no more than two rows tall, so its queen is 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 #93

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

Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 7 rows. By contrast row 4 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.

Working through the middle game

The middle of #93 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.

Keep alternating between two views of the board. In the region view you ask which of the eight colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 8x8 board unwinds.

The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.

Why puzzle #93 is rated hard

What earns a board its rating is the shape of its opening. Here that opening offers no single-line region at all, a 3-square smallest color, a tightest row touched by 3 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 #93 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.

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 #93, start hunting for it near column 4.

As a sanity check rather than a spoiler: the finished solution to #93 puts 4 queens on the outer border and 4 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.

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 #93?

Puzzle #93 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and no region is confined to a single row or column, so the opening move takes some hunting.

Does 8x8 puzzle #93 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #93, 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 #93?

Start with the mint region — the most constrained color on this board, with 3 squares spanning rows 3–4 and columns 5–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.