11x11 Queens Puzzle #105

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 13-step reasoning is written out below.

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Step-by-step solution for puzzle #105

What follows is a complete solve of puzzle #105, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 11 queen placements and 2 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 confined to one line.

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

Show the full walkthrough (7 steps) — contains the solution

  1. Step 1. Only row 3, column 1 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 1, the rest of the blue 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 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 11, the remaining sea green squares, and the ring of neighbours around row 10, column 11.

  3. Step 3. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 7 squares in all.

  4. Step 4. The amber region is down to one open square, at row 2, column 4. Every colour holds exactly one queen, so that square is forced. Row 2 and column 4 are now spoken for, along with the squares touching that queen.

    Puzzle #105 after step 4: 3 of 11 queens placed
    The board after step 4 — 3 of 11 queens placed.

  5. Step 5. Only row 1, column 2 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 2, the rest of the indigo region and every square adjacent to it — diagonals included.

  6. Step 6. All of the red region's remaining squares (4 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.

  7. Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: teal has one square left, so its queen takes row 11, column 5; orange has one square left, so its queen takes row 9, column 6; slate has one square left, so its queen takes row 5, column 7; khaki has one square left, so its queen takes row 8, column 8; pale yellow has one square left, so its queen takes row 7, column 10; 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 3. 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 3.

    Puzzle #105 after step 7: 11 of 11 queens placed
    The board after step 7 — 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 #105

Puzzle #105 is one of the easy-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.

Puzzle #105 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 #105 are: blue (1 square), sea green (1 square), indigo (4 squares), amber (5 squares), orange (5 squares), pale yellow (9 squares), teal (14 squares), khaki (17 squares), red (18 squares), slate (21 squares), mint (26 squares). An even split would hand every color 11 squares, so the blue region is running 10 squares under that average while the mint region is the roomiest area on the grid with 26 squares.

Every color takes one queen and one only, whatever its size — which is why the 25 square difference between blue 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.

Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×4 box that encloses it, while khaki is the most scattered at 47% of its 6×6 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

The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.

Blue: 1 square across rows 3–3, columns 1–1. It never leaves row 3, so its queen is locked to that row.

Sea green covers 1 square, spanning 1 row and 1 column (rows 10–10, columns 11–11). It never leaves row 10, so its queen is locked to that row.

Indigo occupies 4 squares within rows 1–1, columns 1–4. It never leaves row 1, so its queen is locked to that row.

Amber: 5 squares across rows 2–3, columns 1–4.

Orange covers 5 squares, spanning 2 rows and 4 columns (rows 8–9, columns 3–6).

Pale yellow occupies 9 squares within rows 6–9, columns 9–11.

Teal: 14 squares across rows 8–11, columns 1–6.

Khaki covers 17 squares, spanning 6 rows and 6 columns (rows 6–11, columns 6–11).

Red occupies 18 squares within rows 3–9, columns 1–4.

Slate: 21 squares across rows 1–8, columns 4–8.

Mint covers 26 squares, spanning 7 rows and 5 columns (rows 1–7, columns 7–11).

Where to start on this board

Blue is the natural opening on #105: it is the smallest region on the grid at 1 square, boxed into rows 3–3 and columns 1–1. 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 blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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, sea green, amber 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 #105

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 5, 7, 8, 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 2 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 8, meeting 6 colors, is the opposite case — the busiest line on #105 and the last one you should expect to crack.

Working through the middle game

The middle of #105 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.

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 #105 is rated easy

Ratings track how generous the opening is. On #105 you get five regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 25-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.

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 easy board from the rest.

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.

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 #105 is row 11.

Here is a shape check that gives nothing away: when #105 is solved, 4 queens sit on the outer edge of the grid and 7 sit inside it, and no queen lands 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 #105?

Puzzle #105 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.

Does 11x11 puzzle #105 have only one solution?

Yes. Every puzzle in the 11x11 collection, including #105, 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 #105?

Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.