8x8 Queens Puzzle #65

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 #65

What follows is a complete solve of puzzle #65, 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: region shadow, last square in a region.

Show the full walkthrough (7 steps) — contains the solution

  1. Step 1. Wherever indigo ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.

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

  3. Step 3. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: slate has one square left, so its queen takes row 5, column 2; indigo has one square left, so its queen takes row 1, column 1; blue has one square left, so its queen takes row 3, column 3; red has one square left, so its queen takes row 6, column 7; amber has one square left, so its queen takes row 2, column 6. 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 2, column 6.

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

    Puzzle #65 after step 4: 5 of 8 queens placed
    The board after step 4 — 5 of 8 queens placed.

  5. Step 5. Only row 8, column 8 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 8, the rest of the khaki 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 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 5, the remaining mint squares, and the ring of neighbours around row 4, column 5.

  7. Step 7. Only row 7, column 4 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 4, in pale yellow and in the ring around that square is now dead.

    Puzzle #65 after step 7: 8 of 8 queens placed
    The board after step 7 — 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 #65

Puzzle #65 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.

As with every puzzle in this collection, #65 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 #65 are: slate (2 squares), indigo (3 squares), red (3 squares), blue (7 squares), khaki (8 squares), amber (10 squares), pale yellow (13 squares), mint (18 squares). An even split would hand every color 8 squares, so the slate region is running 6 squares under that average while the mint region is the roomiest area on the grid with 18 squares.

Every color takes one queen and one only, whatever its size — which is why the 16 square difference between slate and mint 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.

A region's outline can constrain it more than its size does. Here slate is the most solid, filling 100% of its 2×1 box, and blue the most diffuse at 58% of its 4×3 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 #65, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Slate occupies 2 squares within rows 4–5, columns 2–2. It sits wholly inside column 2, so its queen must be in that column.

Indigo: 3 squares across rows 1–2, columns 1–2.

Red covers 3 squares, spanning 2 rows and 2 columns (rows 5–6, columns 7–8).

Blue occupies 7 squares within rows 2–5, columns 1–3.

Khaki: 8 squares across rows 6–8, columns 5–8.

Amber covers 10 squares, spanning 2 rows and 6 columns (rows 1–2, columns 3–8).

Pale yellow occupies 13 squares within rows 5–8, columns 1–5.

Mint: 18 squares across rows 2–6, columns 4–8.

Where to start on this board

Open on the tightest color. Here that is slate, confined to 2 squares between rows 4 and 5 and columns 2 and 2. Its queen has nowhere else to go, which means those 2 rows and 1 column carry more constraint than anywhere else on #65.

Because slate stays inside column 2, its queen belongs to that column and no other region may use it. Cross out the rest of column 2 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.

Work outward to the other flat regions next. Indigo, amber and red 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 #65

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3, 7 and 8 are the narrowest, touched by only 2 colors. Columns 1, 3, 4 and 6 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 5 colors, is the opposite case — the busiest line on #65 and the last one you should expect to crack.

Working through the middle game

After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.

Two checks, run alternately, will carry you through the 64 squares of this grid. First: has any of the eight regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 8x8 boards almost always run one of those checks and forget the other.

Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.

Why puzzle #65 is rated medium

The rating reflects how much the board concedes up front. Puzzle #65 has one region confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 16 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.

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.

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 #65 is row 1.

Here is a shape check that gives nothing away: when #65 is solved, 2 queens sit on the outer edge of the grid and 6 sit inside it, with 2 queens 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 #65?

Puzzle #65 is rated medium. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.

Does 8x8 puzzle #65 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #65, 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 #65?

Start with the slate region — the most constrained color on this board, with 2 squares spanning rows 4–5 and columns 2–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.