11x11 Queens Puzzle #33

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 17-step reasoning is written out below.

Previous puzzle · All 11x11 puzzles · Next puzzle

Step-by-step solution for puzzle #33

What follows is a complete solve of puzzle #33, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 11 queen placements and 6 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 region shadow.

Techniques this board needs: last square in a region, region shadow, region confined to one line.

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

  1. Step 1. Only row 4, column 6 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 6, the rest of the mint 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 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 3, the remaining sea green squares, and the ring of neighbours around row 10, column 3.

  3. Step 3. The indigo region has 3 squares left, spread across rows 1 and 2, columns 1 and 2. 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.

    Puzzle #33 after step 3: 2 of 11 queens placed
    The board after step 3 — 2 of 11 queens placed.

  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. Red is down to 3 candidates in rows 5 and 6, columns 4 and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.

  6. Step 6. The pale yellow region has 3 squares left, spread across rows 7 and 8, columns 10 and 11. 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.

  7. Step 7. Orange cannot leave column 1 — every one of its open squares (4 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 5 squares in all.

    Puzzle #33 after step 7: 2 of 11 queens placed
    The board after step 7 — 2 of 11 queens placed.

  8. Step 8. The indigo region is down to one open square, at row 1, column 2. Every colour holds exactly one queen, so that square is forced. Row 1 and column 2 are now spoken for, along with the squares touching that queen.

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

  10. Step 10. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: 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 11; red has one square left, so its queen takes row 6, column 5; pale yellow has one square left, so its queen takes row 7, column 10; khaki has one square left, so its queen takes row 8, column 7; amber has one square left, so its queen takes row 2, column 9; teal has one square left, so its queen takes row 11, column 8; orange has one square left, so its queen takes row 9, 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 9, column 1.

    Puzzle #33 after step 10: 11 of 11 queens placed
    The board after step 10 — 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 #33

Puzzle #33 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.

There is exactly one way to finish #33, 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 eleven regions is what sets the depth.

How the colors divide this board

From smallest to largest, the regions on puzzle #33 are: mint (1 square), sea green (1 square), pale yellow (3 squares), indigo (6 squares), red (7 squares), amber (8 squares), khaki (12 squares), orange (15 squares), slate (17 squares), blue (20 squares), teal (31 squares). An even split would hand every color 11 squares, so the mint region is running 10 squares under that average while the teal region is the roomiest area on the grid with 31 squares.

Every color takes one queen and one only, whatever its size — which is why the 30 square difference between mint and teal 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.

Shape matters as much as size. The mint region is the most compact color here, filling 100% of the 1×1 box that encloses it, while blue is the most scattered at 42% of its 8×6 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 #33, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Mint: 1 square across rows 4–4, columns 6–6. It never leaves row 4, so its queen is locked to that row.

Sea green covers 1 square, spanning 1 row and 1 column (rows 10–10, columns 3–3). It never leaves row 10, so its queen is locked to that row.

Pale yellow occupies 3 squares within rows 7–8, columns 10–11.

Indigo: 6 squares across rows 1–3, columns 1–3.

Red covers 7 squares, spanning 3 rows and 3 columns (rows 4–6, columns 4–6).

Amber occupies 8 squares within rows 1–3, columns 6–9.

Khaki: 12 squares across rows 7–10, columns 4–7.

Orange covers 15 squares, spanning 7 rows and 4 columns (rows 5–11, columns 1–4).

Slate occupies 17 squares within rows 1–6, columns 7–11.

Blue: 20 squares across rows 1–8, columns 1–6.

Teal covers 31 squares, spanning 7 rows and 8 columns (rows 5–11, columns 4–11).

Where to start on this board

Mint is the natural opening on #33: it is the smallest region on the grid at 1 square, boxed into rows 4–4 and columns 6–6. 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 mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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. Sea green 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 #33

A quick way to find the next move is to count how many different colors touch each line. On this board, row 11 is the narrowest, touched by only 2 colors. Columns 1, 2, 8, 9, 10 and 11 are the tightest columns, with 3 colors.

Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 8 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.

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 eleven colors looking for one with a single square left; sweep the eleven rows and eleven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 11x11 solve from a stalled one.

A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.

Why puzzle #33 is rated hard

The rating reflects how much the board concedes up front. Puzzle #33 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 30 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

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.

Stuck on #33 despite the hard 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 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 #33 is row 11.

Use this as a rough check on your progress: the completed board has 4 queens around the border and 7 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.

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 #33?

Puzzle #33 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.

Does 11x11 puzzle #33 have only one solution?

Yes. Every puzzle in the 11x11 collection, including #33, 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 #33?

Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.