11x11 Queens Puzzle #241
Difficulty: easy. 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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #241
What follows is a complete solve of puzzle #241, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 11 queen placements and 7 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, last square in a row.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 1, column 5 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 5, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The orange region is down to one open square, at row 9, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 9, the remaining orange squares, and the ring of neighbours around row 9, column 9.
Step 3. Mint cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 9 squares in all.
Step 4. Wherever red ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
The board after step 4 — 2 of 11 queens placed. Step 5. Khaki is down to 3 candidates in rows 8 and 10, columns 6 and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about khaki itself.
Step 6. The teal region has 3 squares left, spread across rows 10 and 11, columns 4, 6, and 8. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
Step 7. Wherever khaki ends up among its 2 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 8. Here is the pairing argument. The sea green and teal regions have no open squares outside rows 10 and 11 — 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: 4 squares come off in one stroke.
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: khaki has one square left, so its queen takes row 8, column 7; red has one square left, so its queen takes row 6, column 2; mint has one square left, so its queen takes row 4, column 1; slate has one square left, so its queen takes row 5, column 6; sea green has one square left, so its queen takes row 10, column 3; teal has one square left, so its queen takes row 11, column 8. 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 8.
The board after step 9 — 8 of 11 queens placed. Step 10. Pale yellow cannot leave column 10 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 1 square in all.
Step 11. 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. Cross out the whole of row 2 and column 11, the remaining amber squares, and the ring of neighbours around row 2, column 11.
Step 12. Only row 7, column 10 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 10, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 13. The blue region is down to one open square, at row 3, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 4, the remaining blue squares, and the ring of neighbours around row 3, column 4.
The board after step 13 — 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 #241
Puzzle #241 is one of the easy-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 #241, 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 #241 are: indigo (1 square), orange (1 square), mint (2 squares), red (8 squares), khaki (9 squares), sea green (9 squares), teal (9 squares), slate (10 squares), amber (13 squares), pale yellow (24 squares), blue (35 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the blue region is the roomiest area on the grid with 35 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 indigo, with 1 square, is under far more pressure than blue with 35. A 34-square gap like this one rewards players who start where the choices are fewest.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×1 box that encloses it, while amber is the most scattered at 46% of its 7×4 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
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.
Indigo covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 5–5). It never leaves row 1, so its queen is locked to that row.
Orange occupies 1 square within rows 9–9, columns 9–9. It never leaves row 9, so its queen is locked to that row.
Mint: 2 squares across rows 4–5, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Red covers 8 squares, spanning 5 rows and 3 columns (rows 5–9, columns 1–3).
Khaki occupies 9 squares within rows 8–10, columns 4–8.
Sea green: 9 squares across rows 9–11, columns 1–4.
Teal covers 9 squares, spanning 2 rows and 6 columns (rows 10–11, columns 4–9).
Slate occupies 10 squares within rows 3–8, columns 6–7.
Amber: 13 squares across rows 1–7, columns 8–11.
Pale yellow covers 24 squares, spanning 9 rows and 4 columns (rows 3–11, columns 8–11).
Blue occupies 35 squares within rows 1–8, columns 1–8.
Where to start on this board
Indigo is the natural opening on #241: it is the smallest region on the grid at 1 square, boxed into rows 1–1 and columns 5–5. 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 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. Orange, mint and teal 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 #241
A quick way to find the next move is to count how many different colors touch each line. On this board, row 2 is the narrowest, touched by only 2 colors. Columns 10 and 11 are the tightest columns, with 2 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 5 sits at the far end with 6 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
The middle of #241 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.
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 #241 is rated easy
Ratings track how generous the opening is. On #241 you get five regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 34-square gap between the largest and smallest regions. Those four numbers largely explain the easy 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.
Stuck on #241 despite the easy 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.
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 #241, start hunting for it near row 2.
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
- 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 #241?
Puzzle #241 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #241 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #241, 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 #241?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.