11x11 Queens Puzzle #233

Difficulty: hard. 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 26-step reasoning is written out below.

Previous puzzle · All 11x11 puzzles · Next puzzle

Step-by-step solution for puzzle #233

What follows is a complete solve of puzzle #233, worked the way a person works it rather than the way a computer does. It runs to 26 deductions — 11 queen placements and 15 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 confined to one line, region shadow, pairing argument on rows, pairing argument on columns, proof by contradiction.

Show the full walkthrough (20 steps) — contains the solution

  1. Step 1. Only row 11, column 11 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 11, the rest of the teal 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. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 9 squares in all.

  4. Step 4. Wherever amber 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.

  5. Step 5. Mint is down to 6 candidates in rows 2–4, columns 6–8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.

    Puzzle #233 after step 5: 2 of 11 queens placed
    The board after step 5 — 2 of 11 queens placed.

  6. Step 6. The orange region has 4 squares left, spread across rows 7 and 9, columns 8–10. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.

  7. Step 7. Amber and blue are now boxed into rows 2 and 3 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 3 squares at once.

  8. Step 8. All of the mint region's remaining squares (3 open squares) lie in row 4. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 7 squares come off.

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

  10. Step 10. Wherever red 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.

    Puzzle #233 after step 10: 2 of 11 queens placed
    The board after step 10 — 2 of 11 queens placed.

  11. Step 11. Indigo and red are now boxed into columns 1 and 2 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 7 squares at once.

  12. Step 12. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: slate has one square left, so its queen takes row 5, column 4; amber has one square left, so its queen takes row 2, column 3; indigo has one square left, so its queen takes row 1, column 1; red has one square left, so its queen takes row 6, 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 6, column 2.

  13. Step 13. Wherever khaki ends up among its 2 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.

  14. Step 14. Pale yellow is down to 4 candidates in rows 7–9, columns 6, 8, 9, and 10, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.

  15. Step 15. Now a short proof by contradiction. Suppose the blue queen went to row 3, column 8. Follow the forced moves that would create and column 9 runs out of open squares entirely — impossible. So that square is ruled out for good.

    Puzzle #233 after step 15: 6 of 11 queens placed
    The board after step 15 — 6 of 11 queens placed.

  16. Step 16. Test row 3, column 10 for blue: place a queen there, run the forced consequences through, and column 9 runs out of open squares entirely. The assumption breaks, so the square is eliminated.

  17. Step 17. The blue region is down to one open square, at row 3, column 9. Every colour holds exactly one queen, so that square is forced. Row 3 and column 9 are now spoken for, along with the squares touching that queen.

  18. Step 18. The pale yellow region has 3 squares left, spread across rows 7 and 8, columns 6, 8, and 10. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.

  19. Step 19. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.

  20. Step 20. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: khaki has one square left, so its queen takes row 8, column 6; mint has one square left, so its queen takes row 4, column 7; pale yellow has one square left, so its queen takes row 7, column 8; orange has one square left, so its queen takes row 9, column 10. 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 9, column 10.

    Puzzle #233 after step 20: 11 of 11 queens placed
    The board after step 20 — 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 #233

Puzzle #233 is one of the hard-rated boards in the 11x11 set. Eleven colors divide its 121 squares, and you win by placing eleven 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, #233 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 #233 are: teal (1 square), indigo (2 squares), sea green (3 squares), red (4 squares), mint (8 squares), slate (9 squares), amber (12 squares), blue (14 squares), orange (16 squares), pale yellow (22 squares), khaki (30 squares). An even split would hand every color 11 squares, so the teal region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 30 squares.

Every color takes one queen and one only, whatever its size — which is why the 29 square difference between teal and khaki 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.

Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×2 frame; orange is the loosest, occupying only 57% of its 7×4 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

Region by region

Here is the full footprint of every color on puzzle #233, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Teal occupies 1 square within rows 11–11, columns 11–11. It never leaves row 11, so its queen is locked to that row.

Indigo: 2 squares across rows 1–1, columns 1–2. It never leaves row 1, so its queen is locked to that row.

Sea green covers 3 squares, spanning 2 rows and 2 columns (rows 10–11, columns 4–5).

Red occupies 4 squares within rows 5–7, columns 1–2.

Mint: 8 squares across rows 1–4, columns 6–8.

Slate covers 9 squares, spanning 3 rows and 5 columns (rows 3–5, columns 1–5).

Amber occupies 12 squares within rows 1–3, columns 1–5.

Blue: 14 squares across rows 1–4, columns 7–11.

Orange covers 16 squares, spanning 7 rows and 4 columns (rows 5–11, columns 8–11).

Pale yellow occupies 22 squares within rows 4–9, columns 5–10.

Khaki: 30 squares across rows 5–11, columns 1–7.

Where to start on this board

Teal is the natural opening on #233: it is the smallest region on the grid at 1 square, boxed into rows 11–11 and columns 11–11. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.

Because teal never leaves row 11, its queen must be in that row — and that instantly settles row 11 for everyone else. Sweep along it and X out every square that is not teal. 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 sea green 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 #233

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 8, 9 and 10 are the narrowest, touched by only 3 colors. Columns 3, 6, 9, 10 and 11 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 5, meeting 5 colors, is the opposite case — the busiest line on #233 and the last one you should expect to crack.

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.

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 #233 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 #233 is rated hard

The rating reflects how much the board concedes up front. Puzzle #233 has three 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 29 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

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 hard board from the rest.

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 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.

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 #233 is row 2.

Here is a shape check that gives nothing away: when #233 is solved, 2 queens sit on the outer edge of the grid and 9 sit inside it, with 2 queens 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.

Full rules · Strategy library · Puzzle statistics

Questions about this puzzle

How hard is 11x11 Queens puzzle #233?

Puzzle #233 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.

Does 11x11 puzzle #233 have only one solution?

Yes. Every puzzle in the 11x11 collection, including #233, 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 #233?

Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.