8x8 Queens Puzzle #250

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.

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Step-by-step solution for puzzle #250

What follows is a complete solve of puzzle #250, 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 region shadow.

Techniques this board needs: last square in a region, region shadow, region confined to one line, last square in a row.

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

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

  2. Step 2. 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.

  3. Step 3. Only row 2, column 5 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 5, in amber and in the ring around that square is now dead.

  4. Step 4. Wherever blue 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.

    Puzzle #250 after step 4: 3 of 8 queens placed
    The board after step 4 — 3 of 8 queens placed.

  5. Step 5. Slate is down to 2 candidates in rows 4 and 5, columns 4 and 6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about slate itself.

  6. Step 6. All of the blue region's remaining squares (2 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.

  7. Step 7. Pale yellow cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 4 squares in all.

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

    Puzzle #250 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 #250

Board #250 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, #250 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 #250 are: indigo (1 square), red (1 square), amber (5 squares), pale yellow (7 squares), mint (10 squares), slate (11 squares), khaki (13 squares), blue (16 squares). An even split would hand every color 8 squares, so the indigo region is running 7 squares under that average while the blue region is the roomiest area on the grid with 16 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 1 place to put its queen; blue has 16. The spread between them on this board is 15 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and slate the most diffuse at 44% of its 5×5 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.

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

Red occupies 1 square within rows 6–6, columns 3–3. It never leaves row 6, so its queen is locked to that row.

Amber: 5 squares across rows 1–2, columns 3–5.

Pale yellow covers 7 squares, spanning 4 rows and 3 columns (rows 5–8, columns 1–3).

Mint occupies 10 squares within rows 1–5, columns 1–3.

Slate: 11 squares across rows 2–6, columns 3–7.

Khaki covers 13 squares, spanning 3 rows and 7 columns (rows 6–8, columns 2–8).

Blue occupies 16 squares within rows 1–7, columns 5–8.

Where to start on this board

Indigo is the natural opening on #250: it is the smallest region on the grid at 1 square, boxed into rows 1–1 and columns 8–8. 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 indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Red 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 #250

A quick way to find the next move is to count how many different colors touch each line. On this board, row 8 is the narrowest, touched by only 2 colors. Column 1 is the tightest column, with 2 colors.

Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 7 rows. Row 6 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.

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.

A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.

Why puzzle #250 is rated medium

Ratings track how generous the opening is. On #250 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 15-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.

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.

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.

One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #250 the place to look for one is around row 8.

Use this as a rough check on your progress: the completed board has 3 queens around the border and 5 queens in the middle, including 1 in a corner. 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 #250?

Puzzle #250 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 #250 have only one solution?

Yes. Every puzzle in the 8x8 collection, including #250, 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 #250?

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