8x8 Queens Puzzle #153

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 12-step reasoning is written out below.

Previous puzzle · All 8x8 puzzles · Next puzzle

Step-by-step solution for puzzle #153

What follows is a complete solve of puzzle #153, worked the way a person works it rather than the way a computer does. It runs to 12 deductions — 8 queen placements and 4 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 3, column 8 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 8, the rest of the blue region and every square adjacent to it — diagonals included.

  2. Step 2. The amber region is down to one open square, at row 2, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 6, the remaining amber squares, and the ring of neighbours around row 2, column 6.

  3. Step 3. Only row 8, column 1 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 1, in khaki and in the ring around that square is now dead.

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

    Puzzle #153 after step 4: 3 of 8 queens placed
    The board after step 4 — 3 of 8 queens placed.

  5. Step 5. Red is down to 2 candidates in rows 6 and 7, columns 5 and 7, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about red itself.

  6. Step 6. The pale yellow region has 3 squares left, spread across rows 5 and 7, columns 4 and 5. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.

  7. Step 7. Row 4 has only mint squares left (2 open squares). The row needs a queen and only mint can provide one, which pins that colour to this row and kills its squares elsewhere: 2 squares.

  8. Step 8. 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: column 7 is down to one square, putting a queen on row 6, column 7; slate has one square left, so its queen takes row 5, column 2; mint has one square left, so its queen takes row 4, column 5; pale yellow has one square left, so its queen takes row 7, column 4; indigo has one square left, so its queen takes row 1, column 3. 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 3.

    Puzzle #153 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 #153

Puzzle #153 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.

There is exactly one way to finish #153, 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 #153 are: blue (1 square), khaki (1 square), amber (4 squares), red (8 squares), slate (10 squares), indigo (11 squares), pale yellow (12 squares), mint (17 squares). An even split would hand every color 8 squares, so the blue region is running 7 squares under that average while the mint region is the roomiest area on the grid with 17 squares.

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

Look at arrangement as well as area. Blue is the densest region on this grid at 100% of a 1×1 frame; mint is the loosest, occupying only 47% of its 6×6 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 #153 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.

Blue: 1 square across rows 3–3, columns 8–8. It never leaves row 3, so its queen is locked to that row.

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

Amber occupies 4 squares within rows 1–2, columns 6–8.

Red: 8 squares across rows 4–7, columns 5–8.

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

Indigo occupies 11 squares within rows 1–3, columns 1–7.

Pale yellow: 12 squares across rows 5–8, columns 3–8.

Mint covers 17 squares, spanning 6 rows and 6 columns (rows 2–7, columns 2–7).

Where to start on this board

Open on the tightest color. Here that is blue, confined to 1 square between rows 3 and 3 and columns 8 and 8. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #153.

Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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. Khaki and amber 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 #153

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, 2, 3 and 4 are the tightest columns, with 3 colors.

Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 7 rows. By contrast row 7 meets 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.

Working through the middle game

Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.

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 #153 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 #153 is rated medium

What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 16. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

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.

Stuck on #153 despite the medium 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 #153 is row 1.

As a sanity check rather than a spoiler: the finished solution to #153 puts 3 queens on the outer border and 5 queens in the interior, 1 of them in an actual corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.

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 #153?

Puzzle #153 is rated medium. 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 #153 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #153, 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 #153?

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