8x8 Queens Puzzle #39

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 13-step reasoning is written out below.

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Step-by-step solution for puzzle #39

What follows is a complete solve of puzzle #39, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 8 queen placements and 5 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, region confined to one line, last square in a region.

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

  1. Step 1. Wherever red ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

  2. Step 2. All of the pale yellow region's remaining squares (3 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.

  3. Step 3. Khaki cannot leave row 8 — every one of its open squares (4 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 4 squares in all.

  4. Step 4. All of the red region's remaining squares (2 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.

    Puzzle #39 after step 4: 0 of 8 queens placed
    The board after step 4 — 0 of 8 queens placed.

  5. Step 5. Only row 7, column 1 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 1, the rest of the pale yellow region and every square adjacent to it — diagonals included.

  6. Step 6. The red region is down to one open square, at row 6, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 3, the remaining red squares, and the ring of neighbours around row 6, column 3.

  7. Step 7. Wherever mint 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.

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

    Puzzle #39 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 #39

8x8 puzzle #39 is rated easy. Eight colored regions cover its 64 squares, and your job is to seat eight queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.

There is exactly one way to finish #39, 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 #39 are: pale yellow (3 squares), khaki (4 squares), blue (5 squares), red (5 squares), indigo (9 squares), mint (10 squares), slate (10 squares), amber (18 squares). An even split would hand every color 8 squares, so the pale yellow region is running 5 squares under that average while the amber region is the roomiest area on the grid with 18 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Pale yellow is working with 3 squares while amber has 18 to spare, a gap of 15. 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 pale yellow is the most solid, filling 100% of its 3×1 box, and slate the most diffuse at 50% of its 5×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

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.

Pale yellow: 3 squares across rows 6–8, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.

Khaki covers 4 squares, spanning 1 row and 4 columns (rows 8–8, columns 4–7). It never leaves row 8, so its queen is locked to that row.

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

Red: 5 squares across rows 6–8, columns 2–3.

Indigo covers 9 squares, spanning 3 rows and 4 columns (rows 1–3, columns 5–8).

Mint occupies 10 squares within rows 4–7, columns 3–5.

Slate: 10 squares across rows 4–8, columns 5–8.

Amber covers 18 squares, spanning 5 rows and 5 columns (rows 1–5, columns 1–5).

Where to start on this board

Begin where the choices are fewest. On this board that means pale yellow, which owns just 3 squares inside a 3×1 window running from row 6 to row 8 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Because pale yellow stays inside column 1, its queen belongs to that column and no other region may use it. Cross out the rest of column 1 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. Khaki 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 #39

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

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 8 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.

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 #39 is rated easy

Ratings track how generous the opening is. On #39 you get two regions pinned to a single row or column, a smallest color of 3 squares, a tightest row crossed by 2 colors, and a 15-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.

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.

Stuck on #39 despite the easy 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.

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 row 1 on this board.

A non-spoiling distribution check: solved, #39 carries 4 queens on the perimeter against 4 queens inside, with the corners empty. 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.

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Questions about this puzzle

How hard is 8x8 Queens puzzle #39?

Puzzle #39 is rated easy. Its smallest color region holds 3 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.

Does 8x8 puzzle #39 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #39, 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 #39?

Start with the pale yellow region — the most constrained color on this board, with 3 squares spanning rows 6–8 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.