10x10 Queens Puzzle #239

Difficulty: hard. 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 14-step reasoning is written out below.

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Step-by-step solution for puzzle #239

What follows is a complete solve of puzzle #239, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 10 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 pairing argument on columns.

Techniques this board needs: last square in a region, pairing argument on rows, pairing argument on columns, region shadow, last square in a column.

Show the full walkthrough (6 steps) — contains the solution

  1. Step 1. Only row 6, column 2 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 2, the rest of the red region and every square adjacent to it — diagonals included.

  2. Step 2. Here is the pairing argument. The khaki, orange, and sea green regions have no open squares outside rows 8–10 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 5 squares come off in one stroke.

  3. Step 3. Indigo and khaki are now boxed into columns 1 and 3 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 3 squares at once.

    Puzzle #239 after step 3: 1 of 10 queens placed
    The board after step 3 — 1 of 10 queens placed.

  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.

  5. Step 5. Blue and slate are now boxed into columns 4 and 5 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 8 squares at once.

  6. Step 6. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: sea green has one square left, so its queen takes row 10, column 6; column 3 is down to one square, putting a queen on row 1, column 3; blue has one square left, so its queen takes row 3, column 4; slate has one square left, so its queen takes row 5, column 5; pale yellow has one square left, so its queen takes row 7, column 10; amber has one square left, so its queen takes row 2, column 9; 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; khaki has one square left, so its queen takes row 8, column 1. 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 8, column 1.

    Puzzle #239 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 #239

10x10 puzzle #239 is rated hard. 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, #239 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 #239 are: red (1 square), sea green (6 squares), indigo (7 squares), blue (8 squares), pale yellow (8 squares), amber (10 squares), khaki (10 squares), orange (12 squares), slate (15 squares), mint (23 squares). An even split would hand every color 10 squares, so the red region is running 9 squares under that average while the mint region is the roomiest area on the grid with 23 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Red has only 1 place to put its queen; mint has 23. The spread between them on this board is 22 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

Square count is only half the story — how a color is arranged counts too. Red is the tidiest shape on #239, packing 100% of its 1×1 bounding box, whereas slate straggles across its 6×5 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Here is the full footprint of every color on puzzle #239, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Red occupies 1 square within rows 6–6, columns 2–2. It never leaves row 6, so its queen is locked to that row.

Sea green: 6 squares across rows 8–10, columns 4–6.

Indigo covers 7 squares, spanning 4 rows and 3 columns (rows 1–4, columns 1–3).

Blue occupies 8 squares within rows 1–4, columns 2–5.

Pale yellow: 8 squares across rows 5–7, columns 7–10.

Amber covers 10 squares, spanning 4 rows and 4 columns (rows 1–4, columns 7–10).

Khaki occupies 10 squares within rows 7–10, columns 1–3.

Orange: 12 squares across rows 8–10, columns 6–10.

Slate covers 15 squares, spanning 6 rows and 5 columns (rows 4–9, columns 1–5).

Mint occupies 23 squares within rows 1–8, columns 5–9.

Where to start on this board

Open on the tightest color. Here that is red, confined to 1 square between rows 6 and 6 and columns 2 and 2. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #239.

Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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.

Nothing on this grid is pinned to one or two lines, which is why the opening takes patience. Scan the columns for one where only two or three colors appear — whichever region is forced into it claims that column outright. Chaining two of those observations is normally enough to break #239 open.

The tightest lines on puzzle #239

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5 and 10 are the narrowest, touched by only 3 colors. Columns 1, 4, 6 and 10 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 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 9 rows. By contrast row 8 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.

Working through the middle game

The middle of #239 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.

With ten queens to seat and ten regions competing over 100 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 10x10 boards quickly and players who stall halfway.

Resist the plausible-looking queen. On #239 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 #239 is rated hard

The rating reflects how much the board concedes up front. Puzzle #239 has two regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 22 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

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.

If #239 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 #239 the place to look for one is around row 5.

As a sanity check rather than a spoiler: the finished solution to #239 puts 4 queens on the outer border and 6 queens in the interior, with none in a 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.

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Questions about this puzzle

How hard is 10x10 Queens puzzle #239?

Puzzle #239 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.

Does 10x10 puzzle #239 have only one solution?

Yes. Every puzzle in the 10x10 collection, including #239, 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 #239?

Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 2–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.