11x11 Queens Puzzle #108

Difficulty: medium. 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 #108

What follows is a complete solve of puzzle #108, 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 shadow.

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

Show the full walkthrough (6 steps) — contains the solution

  1. Step 1. Only row 1, column 6 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 6, the rest of the indigo region and every square adjacent to it — diagonals included.

  2. Step 2. The amber region is down to one open square, at row 2, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 1, the remaining amber squares, and the ring of neighbours around row 2, column 1.

  3. Step 3. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 6 squares in all.

    Puzzle #108 after step 3: 2 of 11 queens placed
    The board after step 3 — 2 of 11 queens placed.

  4. Step 4. 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: mint has one square left, so its queen takes row 4, column 11; slate has one square left, so its queen takes row 5, column 7; blue has one square left, so its queen takes row 3, column 5; sea green has one square left, so its queen takes row 10, 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 10, column 10.

  5. Step 5. Red is down to 3 candidates in rows 6 and 7, columns 2 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about red itself.

  6. Step 6. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: khaki has one square left, so its queen takes row 8, column 2; red has one square left, so its queen takes row 6, column 3; orange has one square left, so its queen takes row 9, column 8; pale yellow has one square left, so its queen takes row 7, column 9; teal has one square left, so its queen takes row 11, column 4. 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 11, column 4.

    Puzzle #108 after step 6: 11 of 11 queens placed
    The board after step 6 — 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 #108

This is puzzle number 108 in the 11x11 collection, rated medium. 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 #108 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 #108 are: indigo (1 square), amber (2 squares), sea green (2 squares), khaki (5 squares), mint (10 squares), orange (11 squares), blue (12 squares), slate (14 squares), teal (16 squares), red (18 squares), pale yellow (30 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the pale yellow region is the roomiest area on the grid with 30 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 pale yellow has 30 to spare, a gap of 29. Attack the cramped end and the roomy regions tend to resolve themselves.

A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and orange the most diffuse at 37% of its 5×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

Below is every color on #108 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.

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

Amber covers 2 squares, spanning 2 rows and 1 column (rows 1–2, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.

Sea green occupies 2 squares within rows 10–10, columns 10–11. It never leaves row 10, so its queen is locked to that row.

Khaki: 5 squares across rows 7–9, columns 1–2.

Mint covers 10 squares, spanning 4 rows and 3 columns (rows 1–4, columns 9–11).

Orange occupies 11 squares within rows 6–10, columns 3–8.

Blue: 12 squares across rows 1–3, columns 2–7.

Slate covers 14 squares, spanning 6 rows and 5 columns (rows 1–6, columns 6–10).

Teal occupies 16 squares within rows 9–11, columns 1–7.

Red: 18 squares across rows 3–7, columns 1–5.

Pale yellow covers 30 squares, spanning 7 rows and 7 columns (rows 5–11, columns 5–11).

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 6 and 6. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #108.

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. Sea green and amber 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 #108

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 8, 9 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 1 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.

Two checks, run alternately, will carry you through the 121 squares of this grid. First: has any of the eleven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 11x11 boards almost always run one of those checks and forget the other.

Resist the plausible-looking queen. On #108 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 #108 is rated medium

What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 29. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.

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 11 on this board.

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.

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Questions about this puzzle

How hard is 11x11 Queens puzzle #108?

Puzzle #108 is rated medium. 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 #108 have only one solution?

Yes. Every puzzle in the 11x11 collection, including #108, 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 #108?

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