8x8 Queens Puzzle #138

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.

Previous puzzle · All 8x8 puzzles · Next puzzle

Step-by-step solution for puzzle #138

What follows is a complete solve of puzzle #138, 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 (6 steps) — contains the solution

  1. Step 1. Only row 2, column 7 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 7, the rest of the amber region and every square adjacent to it — diagonals included.

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

  3. Step 3. Only row 3, column 1 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 1, in blue and in the ring around that square is now dead.

    Puzzle #138 after step 3: 2 of 8 queens placed
    The board after step 3 — 2 of 8 queens placed.

  4. Step 4. 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.

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

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

    Puzzle #138 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 #138

Board #138 of the 8x8 bank carries a medium 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, #138 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 #138 are: amber (1 square), khaki (2 squares), blue (5 squares), red (5 squares), indigo (8 squares), mint (12 squares), pale yellow (12 squares), slate (19 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 19 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 amber, with 1 square, is under far more pressure than slate with 19. A 18-square gap like this one rewards players who start where the choices are fewest.

Look at arrangement as well as area. Amber is the densest region on this grid at 100% of a 1×1 frame; mint is the loosest, occupying only 48% 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

Below is every color on #138 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.

Amber: 1 square across rows 2–2, columns 7–7. It never leaves row 2, so its queen is locked to that row.

Khaki covers 2 squares, spanning 2 rows and 1 column (rows 7–8, columns 3–3). It sits wholly inside column 3, so its queen must be in that column.

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

Red: 5 squares across rows 6–8, columns 1–2.

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

Mint occupies 12 squares within rows 2–6, columns 1–5.

Pale yellow: 12 squares across rows 5–8, columns 4–8.

Slate covers 19 squares, spanning 6 rows and 6 columns (rows 2–7, columns 3–8).

Where to start on this board

Amber is the natural opening on #138: it is the smallest region on the grid at 1 square, boxed into rows 2–2 and columns 7–7. 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. Indigo and khaki 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 #138

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 4 are the narrowest, touched by only 2 colors. Columns 1, 2, 6 and 8 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 2, meeting 5 colors, is the opposite case — the busiest line on #138 and the last one you should expect to crack.

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 #138 is rated medium

What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 18. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.

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 #138, start hunting for it near row 1.

Here is a shape check that gives nothing away: when #138 is solved, 4 queens sit on the outer edge of the grid and 4 sit inside it, and no queen lands 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.

Full rules · Strategy library · Puzzle statistics

Questions about this puzzle

How hard is 8x8 Queens puzzle #138?

Puzzle #138 is rated medium. 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 #138 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #138, 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 #138?

Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.