8x8 Queens Puzzle #28

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 11-step reasoning is written out below.

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Step-by-step solution for puzzle #28

What follows is a complete solve of puzzle #28, 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: last square in a region, region confined to one line, region shadow.

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

  1. Step 1. Only row 8, column 2 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 2, the rest of the khaki region and every square adjacent to it — diagonals included.

  2. Step 2. The slate region is down to one open square, at row 5, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 3, the remaining slate squares, and the ring of neighbours around row 5, column 3.

  3. Step 3. 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.

  4. Step 4. All of the mint region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.

    Puzzle #28 after step 4: 3 of 8 queens placed
    The board after step 4 — 3 of 8 queens placed.

  5. Step 5. 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: 2 squares in all.

  6. Step 6. The mint region is down to one open square, at row 4, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 1, the remaining mint squares, and the ring of neighbours around row 4, column 1.

  7. Step 7. Wherever indigo 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.

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

    Puzzle #28 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 #28

This is puzzle number 28 in the 8x8 collection, rated easy. The grid holds 64 squares split between eight colored regions, and a finished board carries eight queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.

There is exactly one way to finish #28, 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 #28 are: khaki (1 square), slate (2 squares), amber (6 squares), blue (8 squares), mint (8 squares), red (10 squares), pale yellow (10 squares), indigo (19 squares). An even split would hand every color 8 squares, so the khaki region is running 7 squares under that average while the indigo region is the roomiest area on the grid with 19 squares.

Every color takes one queen and one only, whatever its size — which is why the 18 square difference between khaki and indigo 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.

Shape matters as much as size. The amber region is the most compact color here, filling 100% of the 3×2 box that encloses it, while blue is the most scattered at 53% of its 5×3 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.

Region by region

Here is the full footprint of every color on puzzle #28, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Khaki covers 1 square, spanning 1 row and 1 column (rows 8–8, columns 2–2). It never leaves row 8, so its queen is locked to that row.

Slate occupies 2 squares within rows 5–5, columns 2–3. It never leaves row 5, so its queen is locked to that row.

Amber: 6 squares across rows 1–3, columns 7–8.

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

Mint occupies 8 squares within rows 4–8, columns 1–2.

Red: 10 squares across rows 6–8, columns 5–8.

Pale yellow covers 10 squares, spanning 4 rows and 4 columns (rows 5–8, columns 3–6).

Indigo occupies 19 squares within rows 1–4, columns 1–6.

Where to start on this board

The most constrained color is where a solve should begin, and on #28 that is khaki with 1 square. It reaches from row 8 to row 8 and from column 2 to column 2 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.

Because khaki never leaves row 8, its queen must be in that row — and that instantly settles row 8 for everyone else. Sweep along it and X out every square that is not khaki. 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. Slate 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 #28

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. Columns 1 and 4 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.

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.

Resist the plausible-looking queen. On #28 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.

Why puzzle #28 is rated easy

The rating reflects how much the board concedes up front. Puzzle #28 has three 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 18 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.

Stuck on #28 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.

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 #28 is row 1.

A non-spoiling distribution check: solved, #28 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 #28?

Puzzle #28 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 #28 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #28, 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 #28?

Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 2–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.