10x10 Queens Puzzle #269

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 19-step reasoning is written out below.

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Step-by-step solution for puzzle #269

What follows is a complete solve of puzzle #269, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 10 queen placements and 9 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: region shadow, region confined to one line, pairing argument on rows, last square in a region, last square in a column.

Show the full walkthrough (10 steps) — contains the solution

  1. Step 1. Wherever indigo ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

  2. Step 2. Pale yellow is down to 4 candidates in rows 6 and 7, columns 1–3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about pale yellow itself.

  3. Step 3. Sea green cannot leave row 10 — every one of its open squares (2 open squares) sits there. That row belongs to sea green, so every square on it owned by another colour is dead: 10 squares in all.

    Puzzle #269 after step 3: 0 of 10 queens placed
    The board after step 3 — 0 of 10 queens placed.

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

  5. Step 5. Orange is down to 3 candidates in rows 8 and 9, columns 5 and 6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about orange itself.

  6. Step 6. Here is the pairing argument. The khaki and orange regions have no open squares outside rows 8 and 9 — 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: 8 squares come off in one stroke.

  7. Step 7. Red and pale yellow are now boxed into rows 6 and 7 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 8 squares at once.

    Puzzle #269 after step 7: 0 of 10 queens placed
    The board after step 7 — 0 of 10 queens placed.

  8. Step 8. All of the slate region's remaining squares (3 open squares) lie in row 5. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.

  9. Step 9. Mint cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 8 squares in all.

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

    Puzzle #269 after step 10: 10 of 10 queens placed
    The board after step 10 — 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 #269

Puzzle #269 is one of the easy-rated boards in the 10x10 set. Ten colors divide its 100 squares, and you win by placing ten 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, #269 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 #269 are: sea green (2 squares), pale yellow (4 squares), indigo (5 squares), mint (9 squares), khaki (9 squares), red (10 squares), slate (11 squares), orange (11 squares), blue (19 squares), amber (20 squares). An even split would hand every color 10 squares, so the sea green region is running 8 squares under that average while the amber region is the roomiest area on the grid with 20 squares.

Every color takes one queen and one only, whatever its size — which is why the 18 square difference between sea green and amber 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.

A region's outline can constrain it more than its size does. Here sea green is the most solid, filling 100% of its 1×2 box, and orange the most diffuse at 46% of its 3×8 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

Below is every color on #269 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.

Sea green occupies 2 squares within rows 10–10, columns 1–2. It never leaves row 10, so its queen is locked to that row.

Pale yellow: 4 squares across rows 6–7, columns 1–3.

Indigo covers 5 squares, spanning 2 rows and 4 columns (rows 1–2, columns 5–8).

Mint occupies 9 squares within rows 3–7, columns 4–6.

Khaki: 9 squares across rows 7–10, columns 1–4.

Red covers 10 squares, spanning 3 rows and 4 columns (rows 6–8, columns 6–9).

Slate occupies 11 squares within rows 5–9, columns 7–10.

Orange: 11 squares across rows 8–10, columns 3–10.

Blue covers 19 squares, spanning 6 rows and 5 columns (rows 1–6, columns 6–10).

Amber occupies 20 squares within rows 1–6, columns 1–4.

Where to start on this board

Begin where the choices are fewest. On this board that means sea green, which owns just 2 squares inside a 1×2 window running from row 10 to row 10 and column 1 to column 2. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Because sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. 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 pale yellow 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 #269

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 4, 9 and 10 are the narrowest, touched by only 3 colors. Columns 5 and 10 are the tightest columns, with 3 colors.

A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 9 rows. Row 6 is the crowded extreme at 6 colors — worth revisiting later, not now.

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 ten colors looking for one with a single square left; sweep the ten rows and ten columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 10x10 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 #269 is rated easy

What earns a board its rating is the shape of its opening. Here that opening offers one single-line region, a 2-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 18. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

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 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.

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 #269 is row 1.

A non-spoiling distribution check: solved, #269 carries 4 queens on the perimeter against 6 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.

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 #269?

Puzzle #269 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.

Does 10x10 puzzle #269 have only one solution?

Yes. Every puzzle in the 10x10 collection, including #269, 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 #269?

Start with the sea green region — the most constrained color on this board, with 2 squares spanning rows 10–10 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.