11x11 Queens Puzzle #2
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #2
What follows is a complete solve of puzzle #2, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 11 queen placements and 9 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 rows.
Techniques this board needs: last square in a region, region shadow, line confined to one region, pairing argument on rows, region confined to one line, last square in a row.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 2, column 8 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 8, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. The red region is down to one open square, at row 6, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 6, the remaining red squares, and the ring of neighbours around row 6, column 6.
Step 3. Only row 10, column 11 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 11, in sea green and in the ring around that square is now dead.
Step 4. Wherever indigo 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.
Step 5. Pale yellow is down to 3 candidates in rows 5 and 7, columns 9 and 10, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
The board after step 5 — 3 of 11 queens placed. Step 6. The khaki region has 6 squares left, spread across rows 7–9, columns 2–4. 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.
Step 7. Wherever orange 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.
Step 8. Every open square left in row 11 (7 open squares) belongs to the teal region. Since that row must contain a queen, teal is the colour that supplies it — so teal squares anywhere else on the board are out, 8 squares in all.
Step 9. Indigo, blue, mint, and slate are now boxed into rows 1, 3, 4, and 5 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 3 squares at once.
The board after step 9 — 3 of 11 queens placed. Step 10. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
Step 11. Khaki is down to 3 candidates in rows 8 and 9, columns 2 and 4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about khaki itself.
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: orange has one square left, so its queen takes row 9, column 1; khaki has one square left, so its queen takes row 8, column 4; row 5 is down to one square, putting a queen on row 5, column 10; pale yellow has one square left, so its queen takes row 7, column 9. 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 7, column 9.
Step 13. Wherever blue 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.
Step 14. 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 2; indigo has one square left, so its queen takes row 1, column 3; blue has one square left, so its queen takes row 3, column 5; teal has one square left, so its queen takes row 11, column 7. 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 7.
The board after step 14 — 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 #2
Board #2 of the 11x11 bank carries a hard 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, #2 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 #2 are: amber (1 square), red (1 square), sea green (1 square), indigo (6 squares), pale yellow (10 squares), orange (12 squares), khaki (13 squares), blue (14 squares), mint (14 squares), slate (19 squares), teal (30 squares). An even split would hand every color 11 squares, so the amber region is running 10 squares under that average while the teal region is the roomiest area on the grid with 30 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 amber, with 1 square, is under far more pressure than teal with 30. A 29-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. Amber is the tidiest shape on #2, packing 100% of its 1×1 bounding box, whereas orange straggles across its 6×5 box at just 40%. 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.
Amber occupies 1 square within rows 2–2, columns 8–8. It never leaves row 2, so its queen is locked to that row.
Red: 1 square across rows 6–6, columns 6–6. It never leaves row 6, 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 6 squares within rows 1–3, columns 2–5.
Pale yellow: 10 squares across rows 5–8, columns 7–11.
Orange covers 12 squares, spanning 6 rows and 5 columns (rows 5–10, columns 1–5).
Khaki occupies 13 squares within rows 6–9, columns 2–7.
Blue: 14 squares across rows 1–5, columns 4–8.
Mint covers 14 squares, spanning 5 rows and 6 columns (rows 1–5, columns 1–6).
Slate occupies 19 squares within rows 1–6, columns 8–11.
Teal: 30 squares across rows 8–11, columns 1–11.
Where to start on this board
Begin where the choices are fewest. On this board that means amber, which owns just 1 square inside a 1×1 window running from row 2 to row 2 and column 8 to column 8. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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. Red 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 #2
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 1 color. Columns 1, 9 and 10 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 1 color, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 6 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
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.
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 #2 is rated hard
Ratings track how generous the opening is. On #2 you get six regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 1 color, and a 29-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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.
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 #2, start hunting for it near row 11.
As a sanity check rather than a spoiler: the finished solution to #2 puts 4 queens on the outer border and 7 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
How to play Queens
- The board is an N×N grid divided into N colored regions.
- Place exactly one queen (♛) in each row, each column, and each colored region.
- No two queens may touch each other — not horizontally, vertically, or diagonally.
- 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.
- 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 #2?
Puzzle #2 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 1 color, and six of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #2 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #2, 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 #2?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.