11x11 Queens Puzzle #284

Difficulty: easy. Place 11 queens on this 11x11 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 22-step reasoning is written out below.

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Step-by-step solution for puzzle #284

What follows is a complete solve of puzzle #284, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 11 queen placements and 11 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 proof by contradiction.

Techniques this board needs: last square in a region, region shadow, region confined to one line, pairing argument on rows, pairing argument on columns, proof by contradiction.

Show the full walkthrough (14 steps) — contains the solution

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

  2. Step 2. The khaki region is down to one open square, at row 8, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 11, the remaining khaki squares, and the ring of neighbours around row 8, column 11.

  3. Step 3. The amber region has 3 squares left, spread across rows 2–4, columns 2 and 3. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.

  4. Step 4. Wherever blue ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.

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

    Puzzle #284 after step 5: 2 of 11 queens placed
    The board after step 5 — 2 of 11 queens placed.

  6. Step 6. Here is the pairing argument. The pale yellow, orange, sea green, and teal regions have no open squares outside rows 7, 9, 10, and 11 — 4 colours confined to 4 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.

  7. Step 7. Wherever slate 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.

  8. Step 8. Red is down to 3 candidates in rows 5 and 6, columns 9 and 10, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about red itself.

  9. Step 9. Slate and red are now boxed into rows 5 and 6 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 7 squares at once.

    Puzzle #284 after step 9: 2 of 11 queens placed
    The board after step 9 — 2 of 11 queens placed.

  10. Step 10. Here is the pairing argument. The amber, slate, and pale yellow regions have no open squares outside columns 2–4 — 3 colours confined to 3 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 6 squares come off in one stroke.

  11. Step 11. Teal is down to 5 candidates in rows 9–11, columns 6–8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about teal itself.

  12. Step 12. Now a short proof by contradiction. Suppose the amber queen went to row 3, column 2. Follow the forced moves that would create and column 4 runs out of open squares entirely — impossible. So that square is ruled out for good.

  13. Step 13. Test row 4, column 2 for amber: place a queen there, run the forced consequences through, and column 4 runs out of open squares entirely. The assumption breaks, so the square is eliminated.

  14. Step 14. 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: amber has one square left, so its queen takes row 2, column 3; 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 9; red has one square left, so its queen takes row 6, column 10; slate has one square left, so its queen takes row 5, column 2; pale yellow has one square left, so its queen takes row 7, column 4; orange has one square left, so its queen takes row 9, column 5; teal has one square left, so its queen takes row 11, column 6; sea green has one square left, so its queen takes row 10, column 8. 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 8.

    Puzzle #284 after step 14: 11 of 11 queens placed
    The board after step 14 — 11 of 11 queens placed.

That completes the board: 11 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 11x11 Queens puzzle #284

This is puzzle number 284 in the 11x11 collection, rated easy. The grid holds 121 squares split between eleven colored regions, and a finished board carries eleven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.

Puzzle #284 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.

How the colors divide this board

From smallest to largest, the regions on puzzle #284 are: indigo (1 square), khaki (1 square), blue (4 squares), orange (5 squares), amber (8 squares), slate (9 squares), teal (10 squares), sea green (13 squares), red (14 squares), pale yellow (15 squares), mint (41 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the mint region is the roomiest area on the grid with 41 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Indigo is working with 1 square while mint has 41 to spare, a gap of 40. Attack the cramped end and the roomy regions tend to resolve themselves.

Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×1 box that encloses it, while orange is the most scattered at 56% of its 3×3 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.

Region by region

Here is the full footprint of every color on puzzle #284, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

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

Khaki: 1 square across rows 8–8, columns 11–11. It never leaves row 8, so its queen is locked to that row.

Blue covers 4 squares, spanning 3 rows and 2 columns (rows 1–3, columns 6–7).

Orange occupies 5 squares within rows 7–9, columns 5–7.

Amber: 8 squares across rows 1–4, columns 1–3.

Slate covers 9 squares, spanning 4 rows and 4 columns (rows 4–7, columns 1–4).

Teal occupies 10 squares within rows 9–11, columns 4–8.

Sea green: 13 squares across rows 9–11, columns 7–11.

Red covers 14 squares, spanning 4 rows and 6 columns (rows 5–8, columns 6–11).

Pale yellow occupies 15 squares within rows 7–11, columns 1–4.

Mint: 41 squares across rows 1–6, columns 3–11.

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 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #284.

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. Khaki is no more than two rows tall, so its queen is 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 #284

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 3, 4, 5, 6, 10 and 11 are the narrowest, touched by only 3 colors. Columns 2, 5, 9 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 3 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 9, meeting 4 colors, is the opposite case — the busiest line on #284 and the last one you should expect to crack.

Working through the middle game

After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.

With eleven queens to seat and eleven regions competing over 121 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 11x11 boards quickly and players who stall halfway.

Resist the plausible-looking queen. On #284 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 #284 is rated easy

The rating reflects how much the board concedes up front. Puzzle #284 has four 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 40 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.

When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.

Techniques that work well at 11x11

At 11x11 you are managing 121 squares, and holding the whole board in your head will not work. Split it into quadrants and solve locally. Most useful deductions on a grid this large are regional — a color pinched between two placed queens, or a band of rows that two regions must share. Trust the marks on the board over your memory.

Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 2 on this board.

Here is a shape check that gives nothing away: when #284 is solved, 3 queens sit on the outer edge of the grid and 8 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 11x11 Queens puzzle #284?

Puzzle #284 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.

Does 11x11 puzzle #284 have only one solution?

Yes. Every puzzle in the 11x11 collection, including #284, has been verified to have exactly one valid arrangement of eleven queens, and it can always be reached by logic alone — no guessing or backtracking needed.

Where should I place my first queen on puzzle #284?

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