10x10 Queens Puzzle #255

Difficulty: easy. Place 10 queens on this 10x10 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 13-step reasoning is written out below.

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Step-by-step solution for puzzle #255

What follows is a complete solve of puzzle #255, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 10 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 1, column 3 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 3, the rest of the indigo region and every square adjacent to it — diagonals included.

  2. Step 2. The sea green region is down to one open square, at row 10, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 1, the remaining sea green squares, and the ring of neighbours around row 10, column 1.

  3. Step 3. Blue cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 4 squares in all.

    Puzzle #255 after step 3: 2 of 10 queens placed
    The board after step 3 — 2 of 10 queens placed.

  4. Step 4. Wherever khaki ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

  5. Step 5. Orange cannot leave row 9 — every one of its open squares (2 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 7 squares in all.

  6. Step 6. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: 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 10; slate has one square left, so its queen takes row 5, column 9; red has one square left, so its queen takes row 6, column 6; orange has one square left, so its queen takes row 9, column 8; mint has one square left, so its queen takes row 4, column 7; blue has one square left, so its queen takes row 3, column 2; amber has one square left, so its queen takes row 2, column 5. 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 2, column 5.

    Puzzle #255 after step 6: 10 of 10 queens placed
    The board after step 6 — 10 of 10 queens placed.

That completes the board: 10 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 10x10 Queens puzzle #255

10x10 puzzle #255 is rated easy. Ten colored regions cover its 100 squares, and your job is to seat ten queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.

Like every board on this site, #255 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.

How the colors divide this board

From smallest to largest, the regions on puzzle #255 are: indigo (1 square), sea green (1 square), slate (5 squares), pale yellow (5 squares), orange (7 squares), blue (11 squares), khaki (12 squares), amber (13 squares), red (17 squares), mint (28 squares). An even split would hand every color 10 squares, so the indigo region is running 9 squares under that average while the mint region is the roomiest area on the grid with 28 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; mint has 28. The spread between them on this board is 27 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×1 frame; mint is the loosest, occupying only 40% of its 7×10 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

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

Sea green covers 1 square, spanning 1 row and 1 column (rows 10–10, columns 1–1). It never leaves row 10, so its queen is locked to that row.

Slate occupies 5 squares within rows 5–7, columns 9–10.

Pale yellow: 5 squares across rows 7–10, columns 9–10.

Orange covers 7 squares, spanning 2 rows and 5 columns (rows 9–10, columns 5–9).

Blue occupies 11 squares within rows 1–4, columns 1–4.

Khaki: 12 squares across rows 8–10, columns 1–5.

Amber covers 13 squares, spanning 4 rows and 5 columns (rows 1–4, columns 3–7).

Red occupies 17 squares within rows 6–9, columns 2–8.

Mint: 28 squares across rows 1–7, columns 1–10.

Where to start on this board

Open on the tightest color. Here that is indigo, confined to 1 square between rows 1 and 1 and columns 3 and 3. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #255.

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. Sea green and orange 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 #255

A quick way to find the next move is to count how many different colors touch each line. On this board, row 5 is the narrowest, touched by only 2 colors. Columns 8 and 10 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 9 rows. Row 10, meeting 4 colors, is the opposite case — the busiest line on #255 and the last one you should expect to crack.

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.

Keep alternating between two views of the board. In the region view you ask which of the ten 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 10x10 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 #255 is rated easy

Ratings track how generous the opening is. On #255 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 27-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.

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.

If #255 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.

Techniques that work well at 10x10

At 10x10 a full re-scan after every move starts to get slow, so work locally instead. Once a queen goes down, check only the regions, rows and columns that placement actually touched — that is where new information appeared. Fall back to a complete sweep only when the local pass turns up nothing, and your solve times will drop noticeably.

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 #255 the place to look for one is around row 5.

Here is a shape check that gives nothing away: when #255 is solved, 3 queens sit on the outer edge of the grid and 7 sit inside it, with 1 queen 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.

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Questions about this puzzle

How hard is 10x10 Queens puzzle #255?

Puzzle #255 is rated easy. 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 10x10 puzzle #255 have only one solution?

Yes. Every puzzle in the 10x10 collection, including #255, has been verified to have exactly one valid arrangement of ten queens, and it can always be reached by logic alone — no guessing or backtracking needed.

Where should I place my first queen on puzzle #255?

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