11x11 Queens Puzzle #281
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 23-step reasoning is written out below.
Previous puzzle · All 11x11 puzzles · Next puzzle
Step-by-step solution for puzzle #281
What follows is a complete solve of puzzle #281, worked the way a person works it rather than the way a computer does. It runs to 23 deductions — 11 queen placements and 12 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 proof by contradiction.
Techniques this board needs: last square in a region, region shadow, pairing argument on rows, region confined to one line, last square in a row, proof by contradiction, line confined to one region.
Show the full walkthrough (18 steps) — contains the solution
Step 1. Only row 3, column 8 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 8, the rest of the blue region and every square adjacent to it — diagonals included.
Step 2. Amber is down to 4 candidates in rows 1 and 2, columns 9–11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The orange region has 3 squares left, spread across rows 8 and 9, 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.
Step 4. Here is the pairing argument. The indigo and amber regions have no open squares outside rows 1 and 2 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 6 squares come off in one stroke.
Step 5. Only row 4, column 2 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 2, the rest of the mint region and every square adjacent to it — diagonals included.
The board after step 5 — 2 of 11 queens placed. Step 6. The slate region has 3 squares left, spread across rows 5 and 6, columns 1, 3, and 4. 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.
Step 7. Orange cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 3 squares in all.
Step 8. The teal region is down to one open square, at row 11, column 3. Every colour holds exactly one queen, so that square is forced. Row 11 and column 3 are now spoken for, along with the squares touching that queen.
Step 9. Only row 5, column 4 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 4, the rest of the slate region and every square adjacent to it — diagonals included.
The board after step 9 — 4 of 11 queens placed. Step 10. Row 2 has a single open square left, at column 11 in the amber region. Every row needs a queen, so this one is forced. Row 2 and column 11 are now spoken for, along with the squares touching that queen.
Step 11. Khaki is down to 6 candidates in rows 6–10, columns 9 and 10, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about khaki itself.
Step 12. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 5. Follow the forced moves that would create and column 10 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 13. Column 5 has only pale yellow squares left (4 open squares). The column needs a queen and only pale yellow can provide one, which pins that colour to this column and kills its squares elsewhere: 2 squares.
Step 14. Now a short proof by contradiction. Suppose the red queen went to row 6, column 6. Follow the forced moves that would create and row 7 runs out of open squares entirely — impossible. So that square is ruled out for good.
The board after step 14 — 5 of 11 queens placed. Step 15. Test row 6, column 10 for red: place a queen there, run the forced consequences through, and the sea green region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 16. Wherever red 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 17. Column 10 has only khaki squares left (3 open squares). The column needs a queen and only khaki can provide one, which pins that colour to this column and kills its squares elsewhere: 3 squares.
Step 18. 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: row 6 is down to one square, putting a queen on row 6, column 7; indigo has one square left, so its queen takes row 1, column 6; sea green has one square left, so its queen takes row 10, column 9; khaki has one square left, so its queen takes row 8, column 10; orange has one square left, so its queen takes row 9, column 1; pale yellow has one square left, so its queen takes row 7, column 5. 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 5.
The board after step 18 — 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 #281
Puzzle #281 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.
There is exactly one way to finish #281, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these eleven regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #281 are: blue (1 square), orange (3 squares), teal (6 squares), amber (7 squares), mint (7 squares), slate (12 squares), khaki (14 squares), indigo (15 squares), sea green (15 squares), pale yellow (19 squares), red (22 squares). An even split would hand every color 11 squares, so the blue region is running 10 squares under that average while the red region is the roomiest area on the grid with 22 squares.
Every color takes one queen and one only, whatever its size — which is why the 21 square difference between blue and red 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 blue region is the most compact color here, filling 100% of the 1×1 box that encloses it, while sea green is the most scattered at 42% 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
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.
Blue occupies 1 square within rows 3–3, columns 8–8. It never leaves row 3, so its queen is locked to that row.
Orange: 3 squares across rows 8–9, columns 1–2.
Teal covers 6 squares, spanning 3 rows and 3 columns (rows 9–11, columns 1–3).
Amber occupies 7 squares within rows 1–3, columns 9–11.
Mint: 7 squares across rows 1–4, columns 1–2.
Slate covers 12 squares, spanning 5 rows and 4 columns (rows 3–7, columns 1–4).
Khaki occupies 14 squares within rows 4–10, columns 9–11.
Indigo: 15 squares across rows 1–3, columns 3–10.
Sea green covers 15 squares, spanning 6 rows and 6 columns (rows 6–11, columns 6–11).
Pale yellow occupies 19 squares within rows 7–11, columns 2–7.
Red: 22 squares across rows 2–7, columns 4–10.
Where to start on this board
Blue is the natural opening on #281: it is the smallest region on the grid at 1 square, boxed into rows 3–3 and columns 8–8. 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. Orange is no more than two rows tall, so its queen is 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 #281
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 5 and 11 are the narrowest, touched by only 3 colors. Columns 5 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 3, meeting 6 colors, is the opposite case — the busiest line on #281 and the last one you should expect to crack.
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.
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 #281 is rated hard
The hard label comes out of four measurable things about #281: two 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 21. Boards that score tight on those measures give up their first queen fast.
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 hard board from the rest.
Stuck on #281 despite the hard rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 #281 is row 1.
Here is a shape check that gives nothing away: when #281 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
- 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 11x11 Queens puzzle #281?
Puzzle #281 is rated hard. 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 #281 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #281, 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 #281?
Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.