8x8 Queens Puzzle #86

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 14-step reasoning is written out below.

Previous puzzle · All 8x8 puzzles · Next puzzle

Step-by-step solution for puzzle #86

What follows is a complete solve of puzzle #86, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 8 queen placements and 6 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 line confined to one region.

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

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

  1. Step 1. Only row 2, column 6 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 6, the rest of the amber region and every square adjacent to it — diagonals included.

  2. Step 2. All of the blue region's remaining squares (3 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.

  3. Step 3. 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: 8 squares in all.

  4. Step 4. Wherever pale yellow ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

    Puzzle #86 after step 4: 1 of 8 queens placed
    The board after step 4 — 1 of 8 queens placed.

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

  6. Step 6. Every open square left in row 1 (4 open squares) belongs to the indigo region. Since that row must contain a queen, indigo is the colour that supplies it — so indigo squares anywhere else on the board are out, 1 square in all.

  7. Step 7. Column 7 has only slate squares left (3 open squares). The column needs a queen and only slate can provide one, which pins that colour to this column and kills its squares elsewhere: 3 squares.

  8. Step 8. 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 5 is down to one square, putting a queen on row 7, column 5; red has one square left, so its queen takes row 6, column 3; khaki has one square left, so its queen takes row 8, column 1; slate has one square left, so its queen takes row 5, column 7; 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 2; 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 #86 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 #86

Board #86 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, #86 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 #86 are: amber (1 square), red (2 squares), blue (3 squares), pale yellow (6 squares), khaki (6 squares), mint (9 squares), indigo (12 squares), slate (25 squares). An even split would hand every color 8 squares, so the amber region is running 7 squares under that average while the slate region is the roomiest area on the grid with 25 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Amber is working with 1 square while slate has 25 to spare, a gap of 24. Attack the cramped end and the roomy regions tend to resolve themselves.

A region's outline can constrain it more than its size does. Here amber is the most solid, filling 100% of its 1×1 box, and pale yellow the most diffuse at 50% of its 3×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

Here is the full footprint of every color on puzzle #86, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Amber occupies 1 square within rows 2–2, columns 6–6. It never leaves row 2, so its queen is locked to that row.

Red: 2 squares across rows 6–6, columns 3–4. It never leaves row 6, so its queen is locked to that row.

Blue covers 3 squares, spanning 3 rows and 1 column (rows 3–5, columns 8–8). It sits wholly inside column 8, so its queen must be in that column.

Pale yellow occupies 6 squares within rows 6–8, columns 2–5.

Khaki: 6 squares across rows 6–8, columns 1–3.

Mint covers 9 squares, spanning 3 rows and 4 columns (rows 3–5, columns 1–4).

Indigo occupies 12 squares within rows 1–3, columns 1–6.

Slate: 25 squares across rows 1–8, columns 4–8.

Where to start on this board

Amber is the natural opening on #86: it is the smallest region on the grid at 1 square, boxed into rows 2–2 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 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. Red 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 #86

A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Column 7 is the tightest column, with 1 color.

A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 7 rows. Row 6 is the crowded extreme at 4 colors — worth revisiting later, not now.

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 #86 is rated easy

The rating reflects how much the board concedes up front. Puzzle #86 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 24 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

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 easy board from the rest.

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.

Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around column 7 on this board.

A non-spoiling distribution check: solved, #86 carries 3 queens on the perimeter against 5 queens inside, 1 of them cornered. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.

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.

Full rules · Strategy library · Puzzle statistics

Questions about this puzzle

How hard is 8x8 Queens puzzle #86?

Puzzle #86 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.

Does 8x8 puzzle #86 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #86, 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 #86?

Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.