8x8 Queens Puzzle #98

Difficulty: easy. 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 #98

What follows is a complete solve of puzzle #98, 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 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 6 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 6, the rest of the mint region and every square adjacent to it — diagonals included.

  2. Step 2. Blue is down to 4 candidates in rows 3 and 6, columns 4, 5, 7, and 8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.

  3. Step 3. Slate cannot leave row 5 — every one of its open squares (2 open squares) sits there. That row belongs to slate, so every square on it owned by another colour is dead: 5 squares in all.

    Puzzle #98 after step 3: 1 of 8 queens placed
    The board after step 3 — 1 of 8 queens placed.

  4. Step 4. All of the khaki region's remaining squares (3 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.

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

    Puzzle #98 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 #98

Board #98 of the 8x8 bank carries a easy rating. Its 64 squares are shared between eight colored regions, and the solution places eight queens: one per row, one per column, one per region, none of them side by side or corner to corner.

As with every puzzle in this collection, #98 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.

How the colors divide this board

From smallest to largest, the regions on puzzle #98 are: mint (1 square), slate (3 squares), khaki (3 squares), indigo (6 squares), pale yellow (8 squares), red (10 squares), blue (15 squares), amber (18 squares). An even split would hand every color 8 squares, so the mint region is running 7 squares under that average while the amber region is the roomiest area on the grid with 18 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 1 square, is under far more pressure than amber with 18. A 17-square gap like this one rewards players who start where the choices are fewest.

Look at arrangement as well as area. Mint is the densest region on this grid at 100% of a 1×1 frame; blue is the loosest, occupying only 60% of its 5×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

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 occupies 1 square within rows 4–4, columns 6–6. It never leaves row 4, so its queen is locked to that row.

Slate: 3 squares across rows 4–5, columns 1–2.

Khaki covers 3 squares, spanning 1 row and 3 columns (rows 8–8, columns 3–5). It never leaves row 8, so its queen is locked to that row.

Indigo occupies 6 squares within rows 1–2, columns 5–8.

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

Red covers 10 squares, spanning 3 rows and 5 columns (rows 6–8, columns 1–5).

Blue occupies 15 squares within rows 2–6, columns 4–8.

Amber: 18 squares across rows 1–5, columns 1–5.

Where to start on this board

Mint is the natural opening on #98: it is the smallest region on the grid at 1 square, boxed into rows 4–4 and columns 6–6. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.

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. Khaki, indigo and slate 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 #98

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

Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 7 rows. By contrast row 5 meets 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.

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.

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 #98 is rated easy

Ratings track how generous the opening is. On #98 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 17-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.

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.

A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.

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 #98, start hunting for it near row 1.

As a sanity check rather than a spoiler: the finished solution to #98 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 #98?

Puzzle #98 is rated easy. 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 #98 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #98, 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 #98?

Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.