10x10 Queens Puzzle #285

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 10-step reasoning is written out below.

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Step-by-step solution for puzzle #285

What follows is a complete solve of puzzle #285, worked the way a person works it rather than the way a computer does. It runs to 10 deductions, every one of them a forced placement. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the last square in a region.

Techniques this board needs: last square in a region.

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

  1. Step 1. Only row 8, column 6 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 6, the rest of the khaki 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 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 5, the remaining sea green squares, and the ring of neighbours around row 10, column 5.

  3. Step 3. Only row 9, column 1 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 1, in orange and in the ring around that square is now dead.

    Puzzle #285 after step 3: 3 of 10 queens placed
    The board after step 3 — 3 of 10 queens placed.

  4. Step 4. The pale yellow region is down to one open square, at row 7, column 3. Every colour holds exactly one queen, so that square is forced. Row 7 and column 3 are now spoken for, along with the squares touching that queen.

  5. Step 5. Only row 6, column 7 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 7, the rest of the red region and every square adjacent to it — diagonals included.

  6. Step 6. The indigo region is down to one open square, at row 1, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 4, the remaining indigo squares, and the ring of neighbours around row 1, column 4.

  7. Step 7. Only row 5, column 9 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 9, in slate and in the ring around that square is now dead.

    Puzzle #285 after step 7: 7 of 10 queens placed
    The board after step 7 — 7 of 10 queens placed.

  8. Step 8. The blue region is down to one open square, at row 3, column 8. Every colour holds exactly one queen, so that square is forced. Row 3 and column 8 are now spoken for, along with the squares touching that queen.

  9. Step 9. Only row 2, column 10 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 10, the rest of the amber region and every square adjacent to it — diagonals included.

  10. Step 10. The mint region is down to one open square, at row 4, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 2, the remaining mint squares, and the ring of neighbours around row 4, column 2.

    Puzzle #285 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 #285

Puzzle #285 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.

There is exactly one way to finish #285, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these ten regions is what sets the depth.

How the colors divide this board

From smallest to largest, the regions on puzzle #285 are: khaki (1 square), orange (4 squares), sea green (4 squares), indigo (5 squares), amber (9 squares), blue (10 squares), pale yellow (10 squares), slate (12 squares), red (17 squares), mint (28 squares). An even split would hand every color 10 squares, so the khaki region is running 9 squares under that average while the mint region is the roomiest area on the grid with 28 squares.

Every color takes one queen and one only, whatever its size — which is why the 27 square difference between khaki and mint 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 khaki is the most solid, filling 100% of its 1×1 box, and red the most diffuse at 49% of its 5×7 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

Here is the full footprint of every color on puzzle #285, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Khaki: 1 square across rows 8–8, columns 6–6. It never leaves row 8, so its queen is locked to that row.

Orange covers 4 squares, spanning 2 rows and 3 columns (rows 9–10, columns 1–3).

Sea green occupies 4 squares within rows 8–10, columns 5–6.

Indigo: 5 squares across rows 1–2, columns 4–7.

Amber covers 9 squares, spanning 5 rows and 3 columns (rows 1–5, columns 8–10).

Blue occupies 10 squares within rows 2–4, columns 6–9.

Pale yellow: 10 squares across rows 7–10, columns 1–4.

Slate covers 12 squares, spanning 4 rows and 5 columns (rows 5–8, columns 6–10).

Red occupies 17 squares within rows 6–10, columns 4–10.

Mint: 28 squares across rows 1–7, columns 1–5.

Where to start on this board

Begin where the choices are fewest. On this board that means khaki, which owns just 1 square inside a 1×1 window running from row 8 to row 8 and column 6 to column 6. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

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 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 #285

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 and 6 are the narrowest, touched by only 3 colors. Columns 1, 2, 3 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 8 is the crowded extreme at 5 colors — worth revisiting later, not now.

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.

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 #285 is rated easy

The rating reflects how much the board concedes up front. Puzzle #285 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 27 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.

Stuck on #285 despite the easy rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.

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 #285 is row 1.

A non-spoiling distribution check: solved, #285 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 #285?

Puzzle #285 is rated easy. 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 #285 have only one solution?

Yes. Every puzzle in the 10x10 collection, including #285, 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 #285?

Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.