8x8 Queens Puzzle #253

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 #253

What follows is a complete solve of puzzle #253, 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 pairing argument on rows.

Techniques this board needs: last square in a region, region shadow, line confined to one region, pairing argument on rows, last square in a column.

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

  1. Step 1. Only row 8, column 4 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 4, the rest of the khaki region and every square adjacent to it — diagonals included.

  2. Step 2. The indigo region is down to one open square, at row 1, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 5, the remaining indigo squares, and the ring of neighbours around row 1, column 5.

  3. Step 3. Only row 2, column 7 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 7, in amber and in the ring around that square is now dead.

  4. Step 4. Wherever pale yellow ends up among its 2 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.

    Puzzle #253 after step 4: 3 of 8 queens placed
    The board after step 4 — 3 of 8 queens placed.

  5. Step 5. Row 3 has only blue squares left (3 open squares). The row needs a queen and only blue can provide one, which pins that colour to this row and kills its squares elsewhere: 3 squares.

  6. Step 6. Here is the pairing argument. The red and pale yellow regions have no open squares outside rows 6 and 7 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 2 squares come off in one stroke.

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

    Puzzle #253 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 #253

Puzzle #253 is one of the easy-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, #253 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 #253 are: khaki (1 square), indigo (2 squares), amber (4 squares), pale yellow (8 squares), mint (10 squares), red (10 squares), slate (14 squares), blue (15 squares). An even split would hand every color 8 squares, so the khaki region is running 7 squares under that average while the blue region is the roomiest area on the grid with 15 squares.

Every color takes one queen and one only, whatever its size — which is why the 14 square difference between khaki and blue 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.

Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #253, packing 100% of its 1×2 bounding box, whereas slate straggles across its 6×6 box at just 39%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a easy board.

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

Indigo occupies 2 squares within rows 1–1, columns 4–5. It never leaves row 1, so its queen is locked to that row.

Amber: 4 squares across rows 1–2, columns 6–8.

Pale yellow covers 8 squares, spanning 3 rows and 4 columns (rows 6–8, columns 1–4).

Mint occupies 10 squares within rows 2–5, columns 6–8.

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

Slate covers 14 squares, spanning 6 rows and 6 columns (rows 2–7, columns 1–6).

Blue occupies 15 squares within rows 1–5, columns 1–4.

Where to start on this board

Open on the tightest color. Here that is khaki, confined to 1 square between rows 8 and 8 and columns 4 and 4. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #253.

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. Indigo 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 #253

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3, 4, 5, 6, 7 and 8 are the narrowest, touched by only 3 colors. Columns 1, 2, 3, 5, 7 and 8 are the tightest columns, with 3 colors.

Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 7 rows. Row 2 sits at the far end with 4 colors crossing it; it will almost certainly be among the last to settle.

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.

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.

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 #253 is rated easy

The easy label comes out of four measurable things about #253: three of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 14. Boards that score tight on those measures give up their first queen fast.

Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.

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 #253 is row 1.

Use this as a rough check on your progress: the completed board has 4 queens around the border and 4 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.

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 #253?

Puzzle #253 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.

Does 8x8 puzzle #253 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #253, 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 #253?

Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.