11x11 Queens Puzzle #230
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 25-step reasoning is written out below.
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Step-by-step solution for puzzle #230
What follows is a complete solve of puzzle #230, worked the way a person works it rather than the way a computer does. It runs to 25 deductions — 11 queen placements and 14 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: region shadow, region confined to one line, pairing argument on rows, last square in a region, last square in a row, line confined to one region, last square in a column, proof by contradiction.
Show the full walkthrough (19 steps) — contains the solution
Step 1. Wherever amber ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. All of the slate region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 11 squares come off.
Step 3. The sea green region has 5 squares left, spread across rows 9 and 10, columns 4–7. 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 4. All of the teal region's remaining squares (6 open squares) lie in row 11. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
Step 5. Indigo, amber, and blue are now boxed into rows 1–3 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 9 squares at once.
The board after step 5 — 0 of 11 queens placed. 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: mint has one square left, so its queen takes row 4, column 10; slate has one square left, so its queen takes row 5, column 1; red has one square left, so its queen takes row 6, column 3; row 3 is down to one square, putting a queen on row 3, 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 3, column 2.
Step 7. All of the amber region's remaining squares (2 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
Step 8. Pale yellow cannot leave column 9 — 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: 4 squares in all.
Step 9. The orange region has 3 squares left, spread across rows 7 and 9, columns 4 and 5. 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 10. Row 8 has only khaki squares left (3 open squares). The row needs a queen and only khaki can provide one, which pins that colour to this row and kills its squares elsewhere: 5 squares.
The board after step 10 — 4 of 11 queens placed. Step 11. All of the khaki region's remaining squares (3 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 12. Sea green cannot leave row 10 — every one of its open squares (3 open squares) sits there. That row belongs to sea green, so every square on it owned by another colour is dead: 1 square in all.
Step 13. The pale yellow region is down to one open square, at row 7, column 9. Every colour holds exactly one queen, so that square is forced. Row 7 and column 9 are now spoken for, along with the squares touching that queen.
Step 14. Scan column 8 and only row 1, column 8 remains — a indigo square. Every column takes a queen, so it takes this one. Row 1 and column 8 are now spoken for, along with the squares touching that queen.
The board after step 14 — 6 of 11 queens placed. Step 15. The amber region is down to one open square, at row 2, column 11. Every colour holds exactly one queen, so that square 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 16. Orange cannot leave row 9 — every one of its open squares (2 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 1 square in all.
Step 17. All of the sea green region's remaining squares (2 open squares) lie in row 10. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
Step 18. Test row 8, column 7 for khaki: place a queen there, run the forced consequences through, and column 5 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 19. 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: khaki has one square left, so its queen takes row 8, column 6; 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 7; teal has one square left, so its queen takes row 11, 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 11, column 5.
The board after step 19 — 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 #230
Board #230 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, #230 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 #230 are: slate (2 squares), amber (4 squares), mint (5 squares), sea green (5 squares), red (7 squares), teal (7 squares), blue (9 squares), indigo (11 squares), pale yellow (14 squares), orange (16 squares), khaki (41 squares). An even split would hand every color 11 squares, so the slate region is running 9 squares under that average while the khaki region is the roomiest area on the grid with 41 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 slate, with 2 squares, is under far more pressure than khaki with 41. A 39-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. Blue is the tidiest shape on #230, packing 100% of its 3×3 bounding box, whereas khaki straggles across its 10×10 box at just 41%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #230 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Slate occupies 2 squares within rows 4–5, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Amber: 4 squares across rows 1–3, columns 10–11.
Mint covers 5 squares, spanning 3 rows and 3 columns (rows 2–4, columns 8–10).
Sea green occupies 5 squares within rows 9–10, columns 4–7.
Red: 7 squares across rows 4–6, columns 2–4.
Teal covers 7 squares, spanning 1 row and 7 columns (rows 11–11, columns 1–7). It never leaves row 11, so its queen is locked to that row.
Blue occupies 9 squares within rows 1–3, columns 1–3.
Indigo: 11 squares across rows 1–2, columns 4–10.
Pale yellow covers 14 squares, spanning 7 rows and 3 columns (rows 4–10, columns 9–11).
Orange occupies 16 squares within rows 6–10, columns 1–5.
Khaki: 41 squares across rows 2–11, columns 2–11.
Where to start on this board
Begin where the choices are fewest. On this board that means slate, which owns just 2 squares inside a 2×1 window running from row 4 to row 5 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because slate stays inside column 1, its queen belongs to that column and no other region may use it. Cross out the rest of column 1 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
Work outward to the other flat regions next. Teal, 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 #230
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 2 colors. Columns 8 and 11 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 4 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
The middle of #230 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.
With eleven queens to seat and eleven regions competing over 121 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 11x11 boards quickly and players who stall halfway.
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 #230 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 2-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 39. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
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 #230, start hunting for it near row 11.
A non-spoiling distribution check: solved, #230 carries 4 queens on the perimeter against 7 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
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 #230?
Puzzle #230 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #230 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #230, 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 #230?
Start with the slate region — the most constrained color on this board, with 2 squares spanning rows 4–5 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.