11x11 Queens Puzzle #245
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.
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Step-by-step solution for puzzle #245
What follows is a complete solve of puzzle #245, 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 rows.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Only row 10, column 4 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 4, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 10 squares come off.
Step 3. Amber cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 9 squares in all.
The board after step 3 — 1 of 11 queens placed. Step 4. Wherever slate ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 5. Amber, blue, and mint are now boxed into rows 2–4 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 5 squares at once.
Step 6. 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: slate has one square left, so its queen takes row 5, column 8; red has one square left, so its queen takes row 6, column 11; indigo has one square left, so its queen takes row 1, column 10; pale yellow has one square left, so its queen takes row 7, column 2. 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 2.
The board after step 6 — 5 of 11 queens placed. Step 7. Wherever blue ends up among its 2 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Khaki cannot leave row 8 — every one of its open squares (3 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 2 squares in all.
Step 9. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: orange has one square left, so its queen takes row 9, column 7; blue has one square left, so its queen takes row 3, column 9; amber has one square left, so its queen takes row 2, column 1; khaki has one square left, so its queen takes row 8, column 5; teal has one square left, so its queen takes row 11, column 6; mint has one square left, so its queen takes row 4, 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 4, column 3.
The board after step 9 — 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 #245
Puzzle #245 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.
As with every puzzle in this collection, #245 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 #245 are: sea green (1 square), indigo (2 squares), amber (2 squares), slate (4 squares), red (8 squares), teal (11 squares), blue (13 squares), pale yellow (19 squares), orange (19 squares), mint (21 squares), khaki (21 squares). An even split would hand every color 11 squares, so the sea green region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 21 squares.
Every color takes one queen and one only, whatever its size — which is why the 20 square difference between sea green and khaki 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 1×2 box that encloses it, while pale yellow is the most scattered at 39% of its 7×7 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
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a hard board.
Sea green occupies 1 square within rows 10–10, columns 4–4. It never leaves row 10, so its queen is locked to that row.
Indigo: 2 squares across rows 1–1, columns 10–11. It never leaves row 1, so its queen is locked to that row.
Amber covers 2 squares, spanning 2 rows and 1 column (rows 2–3, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Slate occupies 4 squares within rows 3–5, columns 7–8.
Red: 8 squares across rows 4–6, columns 8–11.
Teal covers 11 squares, spanning 3 rows and 5 columns (rows 9–11, columns 5–9).
Blue occupies 13 squares within rows 1–4, columns 7–11.
Pale yellow: 19 squares across rows 4–10, columns 1–7.
Orange covers 19 squares, spanning 6 rows and 5 columns (rows 6–11, columns 7–11).
Mint occupies 21 squares within rows 1–4, columns 1–6.
Khaki: 21 squares across rows 6–11, columns 1–7.
Where to start on this board
Sea green is the natural opening on #245: it is the smallest region on the grid at 1 square, boxed into rows 10–10 and columns 4–4. 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 sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. 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 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 #245
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 5, 7, 8 and 11 are the narrowest, touched by only 3 colors. Columns 2 and 3 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 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 10 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
The middle of #245 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.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #245 is rated hard
The hard label comes out of four measurable things about #245: four of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 20. Boards that score tight on those measures give up their first queen fast.
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.
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.
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 #245 is row 1.
As a sanity check rather than a spoiler: the finished solution to #245 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 #245?
Puzzle #245 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #245 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #245, 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 #245?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.