11x11 Queens Puzzle #42

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 17-step reasoning is written out below.

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Step-by-step solution for puzzle #42

What follows is a complete solve of puzzle #42, 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 pairing argument on columns.

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

Show the full walkthrough (8 steps) — contains the solution

  1. Step 1. Only row 6, column 10 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 10, the rest of the red region and every square adjacent to it — diagonals included.

  2. Step 2. Indigo is down to 3 candidates in rows 1 and 2, columns 2 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about indigo itself.

  3. Step 3. The sea green region has 3 squares left, spread across rows 9 and 10, columns 1 and 2. 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. Here is the pairing argument. The indigo, amber, and blue regions have no open squares outside rows 1–3 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 13 squares come off in one stroke.

    Puzzle #42 after step 4: 1 of 11 queens placed
    The board after step 4 — 1 of 11 queens placed.

  5. Step 5. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 8 squares in all.

  6. Step 6. Here is the pairing argument. The blue and mint regions have no open squares outside columns 9 and 11 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 8 squares come off in one stroke.

  7. Step 7. Pale yellow and sea green 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 6 squares at once.

  8. Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 10 queens fall out in order without any new idea being needed: indigo has one square left, so its queen takes row 1, column 3; orange has one square left, so its queen takes row 9, column 4; sea green has one square left, so its queen takes row 10, column 1; pale yellow has one square left, so its queen takes row 7, column 2; teal has one square left, so its queen takes row 11, column 5; column 9 is down to one square, putting a queen on row 4, column 9; khaki has one square left, so its queen takes row 8, column 8; amber has one square left, so its queen takes row 2, column 7; blue has one square left, so its queen takes row 3, column 11; slate has one square left, so its queen takes row 5, column 6. 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 5, column 6.

    Puzzle #42 after step 8: 11 of 11 queens placed
    The board after step 8 — 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 #42

Board #42 of the 11x11 bank carries a medium rating. Its 121 squares are shared between eleven colored regions, and the solution places eleven queens: one per row, one per column, one per region, none of them side by side or corner to corner.

As with every puzzle in this collection, #42 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 #42 are: red (1 square), indigo (3 squares), sea green (3 squares), blue (7 squares), amber (8 squares), orange (8 squares), pale yellow (9 squares), teal (9 squares), mint (10 squares), khaki (24 squares), slate (39 squares). An even split would hand every color 11 squares, so the red region is running 10 squares under that average while the slate region is the roomiest area on the grid with 39 squares.

Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So red, with 1 square, is under far more pressure than slate with 39. A 38-square gap like this one rewards players who start where the choices are fewest.

Square count is only half the story — how a color is arranged counts too. Red is the tidiest shape on #42, packing 100% of its 1×1 bounding box, whereas orange straggles across its 4×4 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

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.

Red: 1 square across rows 6–6, columns 10–10. It never leaves row 6, so its queen is locked to that row.

Indigo covers 3 squares, spanning 2 rows and 2 columns (rows 1–2, columns 2–3).

Sea green occupies 3 squares within rows 9–10, columns 1–2.

Blue: 7 squares across rows 1–3, columns 9–11.

Amber covers 8 squares, spanning 3 rows and 5 columns (rows 1–3, columns 4–8).

Orange occupies 8 squares within rows 8–11, columns 1–4.

Pale yellow: 9 squares across rows 4–8, columns 1–3.

Teal covers 9 squares, spanning 3 rows and 5 columns (rows 9–11, columns 3–7).

Mint occupies 10 squares within rows 2–6, columns 9–11.

Khaki: 24 squares across rows 5–11, columns 6–11.

Slate covers 39 squares, spanning 9 rows and 8 columns (rows 1–9, columns 1–8).

Where to start on this board

Begin where the choices are fewest. On this board that means red, which owns just 1 square inside a 1×1 window running from row 6 to row 6 and column 10 to column 10. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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 #42

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 4, 7 and 11 are the narrowest, touched by only 3 colors. Columns 5, 8, 9 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 9, meeting 5 colors, is the opposite case — the busiest line on #42 and the last one you should expect to crack.

Working through the middle game

The middle of #42 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.

Keep alternating between two views of the board. In the region view you ask which of the eleven colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 11x11 board unwinds.

Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.

Why puzzle #42 is rated medium

Ratings track how generous the opening is. On #42 you get two regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 38-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.

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.

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.

Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #42, start hunting for it near row 4.

Here is a shape check that gives nothing away: when #42 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 #42?

Puzzle #42 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.

Does 11x11 puzzle #42 have only one solution?

Yes. Every puzzle in the 11x11 collection, including #42, 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 #42?

Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 10–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.